CRC Press, Taylor & Francis Group, 2014. — XIV, 629 p. — ISBN13: 978-1-4665-1057-9. With a special emphasis on engineering and science applications, this textbook provides a mathematical introduction to PDEs at the undergraduate level. It takes a new approach to PDEs by presenting computation as an integral part of the study of differential equations. The authors use...
Springer, 2019. — 285 p. — (Springer INdAM Series 32). — ISBN: 978-3-030-17948-9. This book presents cutting-edge contributions in the areas of control theory and partial differential equations. Over the decades, control theory has had deep and fruitful interactions with the theory of partial differential equations (PDEs). Well-known examples are the study of the generalized...
Springer, 2012. - 357 pages. ISBN: 3642278922
The term 'control theory' refers to the body of results - theoretical, numerical and algorithmic - which have been developed to influence the evolution of the state of a given system in order to meet a prescribed performance criterion. Systems of interest to control theory may be of very different natures. This monograph is...
Cambridge: Cambridge University Press, 2022. — 390 p. — ISBN 1009201441. Partial differential equations are a vital part of any course in pure or applied mathematics. This book will be invaluable to anyone looking for a lucid but comprehensive introduction to PDEs. Designed to strike a balance between theory and practical problems, it covers all major methods as well as their...
Springer, 2024. - 438 p. - (Universitext). - ISBN 303170908X. This textbook provides a modern introduction to advanced concepts and methods of mathematical analysis. The first three parts of the book cover functional analysis, harmonic analysis, and microlocal analysis. Each chapter is designed to provide readers with a solid understanding of fundamental concepts while guiding...
Springer, 2020. — 362 p. — (Universitext). — ISBN: 978-3-030-50283-6. This textbook offers a unique learning-by-doing introduction to the modern theory of partial differential equations. Through 65 fully solved problems, the book offers readers a fast but in-depth introduction to the field, covering advanced topics in microlocal analysis, including pseudo- and para-differential...
Springer, 2003. — 440 p. This text deals with the singularities of the solutions of several classes of nonlinear partial differential equations and systems. Applications of the results here obtained are given for the Monge-Ampere equation, for quasi-linear systems arising in fluid mechanics, and for some nonlinear integrodifferential equations useful in solid body mechanics in...
Cambridge University Press, 2010. — 128 p. Its self-contained presentation and 'do-it-yourself' approach make this the perfect guide for graduate students and researchers wishing to access recent literature in the field of nonlinear wave equations and general relativity. It introduces all of the key tools and concepts from Lorentzian geometry (metrics, null frames, deformation...
Springer, 2009. — 150 p.
This excellent introduction to hyperbolic differential equations is devoted to linear equations and symmetric systems, as well as conservation laws. The book is divided into two parts. The first, which is intuitive and easy to visualize, includes all aspects of the theory involving vector fields and integral curves; the second describes the wave...
Berlin: de Gruyter, 2021. — 514 p. The scientific literature on the Hardy-Leray inequality, also known as the uncertainty principle, is very extensive and scattered. The Hardy-Leray potential shows an extreme spectral behavior and a peculiar influence on diffusion problems, both stationary and evolutionary. In this book, a big part of the scattered knowledge about these...
Birkhäuser Basel, 2011. — 199 p. — ISBN: 978-0-8176-8114-2 (eBook), 978-0-8176-8113-5 (Hardcover). This self-contained textbook provides the basic, abstracttoolsused innonlinear analysisand their applications to semilinear elliptic boundary value problems.By firstoutlining the advantages and disadvantages of each method, this comprehensive textdisplays how variousapproachescan...
Cambridge University Press, 2007, 316p.
Many problems in science and engineering are described by nonlinear differential equations, which can be notoriously difficult to solve. Through the interplay of topological and variational ideas, methods of nonlinear analysis are able to tackle such fundamental problems. This graduate text explains some of the key techniques in a way...
Springer, 2008. - 204 Pages. This volume provides the texts of lectures given by L. Ambrosio, L. Caffarelli, M. Crandall, L.C. Evans, N. Fusco at the Summer course held in Cetraro (Italy) in 2005. These are introductory reports on current research by world leaders in the fields of calculus of variations and partial differential equations. The topics discussed are transport...
Pisa: Scuola Normale Superiore, 2019. - 230 p. - (Publications of the Scuola Normale Superiore) - ISBN: 8876426507 This text originated from the Ph.D. course given by the first author at the Scuola Normale Superiore in the academic year 2009-2010. The second and third authors, students of S.N.S. at that time, wrote down the first version of the notes. Since then, the course has...
Birkhäuser, 2021. — 669 p. — (Frontiers in Mathematics: Frontiers in Elliptic and Parabolic Problems). — ISBN 978-3030602192. This monograph presents recent results concerning nonlinear fractional elliptic problems in the whole space. More precisely, it investigates the existence, multiplicity and qualitative properties of solutions for fractional Schrödinger equations by...
American Mathematical Society, 2018. — 161 p. — (CRM Monograph Series 37). — ISBN: 1470442507. In this monograph the authors study the well-posedness of boundary value problems of Dirichlet and Neumann type for elliptic systems on the upper half-space with coefficients independent of the transversal variable and with boundary data in fractional Hardy–Sobolev and Besov spaces....
Yale: Yale University Press, 1975. — 30 p. Elementary and Levi Convexity On the Hans Lewy Problem Complexes of Differential Operators with Constant Coefficients Boundary Value Problems for General Complexes of Differential Operators Complexes of Differential Operators with Variable Coefficients
Basel: Birkhäuser, 2004. — 350 p. Award-winning monograph of the Ferran Sunyer i Balaguer Prize 2003. This book contains a detailed mathematical analysis of the variational approach to image restoration based on the minimization of the total variation submitted to the constraints given by the image acquisition model. This model, initially introduced by Rudin, Osher, and Fatemi,...
Atlantis Press, 2015. — 417 p. — (Atlantis Studies in Differential Equations 04). — ISBN 978-94-6239-111-6. This monograph is a contribution to the theory of second order quasilinear parabolic and hyperbolic equations with the nonlinear structure that may change from one point to another in the problem domain. In the past decade, there was an impetuous growth of interest in the...
Cham: Springer, 2023. — 463 p. This textbook introduces the study of partial differential equations using both analytical and numerical methods. By intertwining the two complementary approaches, the authors create an ideal foundation for further study. Motivating examples from the physical sciences, engineering, and economics complete this integrated approach. A showcase of...
Springer, 2004. — 157 p. — ISBN: 3-540-40448-1. Like all of Vladimir Arnold's books, this book is full of geometric insight. Arnold illustrates every principle with a figure. This book aims to cover the most basic parts of the subject and confines itself largely to the Cauchy and Neumann problems for the classical linear equations of mathematical physics, especially Laplace's...
San Rafael: Morgan & Claypool Publishers, 2019. — 166 p. — (Synthesis Lectures on Mathematics and Statistics). — ISBN: 1681735350. This is an introduction to methods for solving nonlinear partial differential equations (NLPDEs). After the introduction of several PDEs drawn from science and engineering, the reader is introduced to techniques used to obtain exact solutions of...
Academic Press, 2009. - 744 pages.
Integrating Maple V animation software and traditional topics of partial differential equations, this text discusses first and second-order differential equations, Sturm-Liouville eigenvalue problems, generalized Fourier series, the diffusion or heat equation and the wave equation in one and two spatial dimensions, the Laplace equation in two...
Springer, 2004. — 443 p. — (Operator Theory: Advances and Applications Vol.148) — ISBN: 978-3-0348-9622-1. The present monograph is devoted to the construction and investigation of the new high order of accuracy difference schemes of approximating the solutions of regular and singular perturbation boundary value problems for partial differential equations. The construction is...
University of Missouri. — 440 p. Решебник к книге /file/1276079/ This manual contains solutions with notes and comments to problems from the textbook "Partial Differential Equations with Fourier Series and Boundary Value Problems" (Second Edition). Most solutions are supplied with complete details and can be used to supplement examples from the text. There are also many figures...
Pearson Education, 2004. — 816 p. — ISBN: 0131480960 Решебник к этой книге: /file/1567779/ This example-rich reference fosters a smooth transition from elementary ordinary differential equations to more advanced concepts. Asmar's relaxed style and emphasis on applications make the material accessible even to readers with limited exposure to topics beyond calculus. Encourages...
New York: Chapman and Hall/CRC, 2019. — 275 p. Spectral Methods Using Multivariate Polynomials on the Unit Ball is a research level text on a numerical method for the solution of partial differential equations. The authors introduce, illustrate with examples, and analyze `spectral methods` that are based on multivariate polynomial approximations. The method presented is an...
Basel: Birkhäuser, 2023. — 310 p. In this monograph, for elliptic systems with block structure in the upper half-space and t-independent coefficients, the authors settle the study of boundary value problems by proving compatible well-posedness of Dirichlet, regularity and Neumann problems in optimal ranges of exponents. Prior to this work, only the two-dimensional situation was...
Cambridge University Press, 2019. — 472 p. — ( London Mathematical Society Lecture Note Series: 450). — ISBN: 978-1-108-43163-7. In this edited volume leaders in the field of partial differential equations present recent work on topics in PDEs arising from geometry and physics. The papers originate from a 2015 research school organized by CIMPA and MIMS in Hammamet, Tunisia to...
Springer, 2010. - 199 pages.
Semilinear elliptic equations are of fundamental importance for the study of geometry, physics, mechanics, engineering and life sciences. The variational approach to these equations has experienced spectacular success in recent years, reaching a high level of complexity and refinement, with a multitude of applications. Additionally, some of the...
Berlin: Springer, 2011. — 540 p. In recent years, the Fourier analysis methods have expereinced a growing interest in the study of partial differential equations. In particular, those techniques based on the Littlewood-Paley decomposition have proved to be very efficient for the study of evolution equations. The present book aims at presenting self-contained, state- of- the-...
Cetraro, Italy 2013. — Springer, 2017. — 250 p. Collating different aspects of Vector-valued Partial Differential Equations and Applications, this volume is based on the 2013 CIME Course with the same name which took place at Cetraro, Italy, under the scientific direction of John Ball and Paolo Marcellini. It contains the following contributions: The pullback equation (Bernard...
Cham: Springer, 2022. — 283 p. This book provides a comprehensive analysis of time domain boundary integral equations and their discretisation by convolution quadrature and the boundary element method. Properties of convolution quadrature, based on both linear multistep and Runge–Kutta methods, are explained in detail, always with wave propagation problems in mind. Main...
Springer International Publishing AG, 2018. — 234 p. — (Progress in Nonlinear Differential Equations and Their Applications: Subseries in Control 90). — ISBN: 3319766651. This monograph presents controllability and stabilization methods in control theory that solve parabolic boundary value problems. Starting from foundational questions on Carleman inequalities for linear...
Springer International Publishing, Switzerland, 2016. — 317 p. — ISBN10: 3319320602 This monograph explores the modeling of conservation and balance laws of one-dimensional hyperbolic systems using partial differential equations. It presents typical examples of hyperbolic systems for a wide range of physical engineering applications, allowing readers to understand the concepts...
Springer, 2022. — 238 p. — (Progress in Nonlinear Differential Equations and Their Applications; PNLDE Subseries in Control 99). — ISBN 9783030930158. Conservation and balance laws on networks have been the subject of much research interest given their wide range of applications to real-world processes, particularly traffic flow. This open access monograph is the first to...
Boca Raton: CRC Press/Chapman & Hall, 1993. — 280 p. Complex analytical methods are a powerful tool for special partial differential equations and systems. To make these methods applicable for a wider class, transformations and transmutations are used. Systems of Elliptic Equations Kernel Functions for Higher-Order Systems Bianalytic Functions Systems of First-Order Equations...
Springer Japan KK, 2017. — 267 p. — (Springer Monographs in Mathematics) — ISBN: 978-4-431-56598-7 In this book, focusing on hyperbolic systems, we give self-contained descriptions of • derivations of Carleman estimates; • methods for application of Carleman estimates to stability of inverse problems. Confining ourselves to equations of hyperbolic type, we survey previous and...
Birkhauser, 2008. — 205 p. This book examines various mathematical tools—based on generalized collocation methods—to solve nonlinear problems related to partial differential and integro-differential equations. Covered are specific problems and models related to vehicular traffic flow, population dynamics, wave phenomena, heat convection and diffusion, transport phenomena, and...
De Gruyter, 2002. — 220 p. Preface Auxiliary information from functional analysis and theory of differential equations The weak approximation method Identification problems for parabolic equations with Cauchy data The identification of the source function for a system of composite type and parabolic equation. The behavior of the problem’s solution under t —> + ∞ The problem of...
Philadelphia, USA: Society for Industrial and Applied Mathematics (SIAM), 2017. — 433 p. — (Computational Science & Engineering). — ISBN: 9781611974812. Many physical, chemical, biomedical, and technical processes can be described by partial differential equations or dynamical systems. In spite of increasing computational capacities, many problems are of such high complexity...
Oxford University Press, USA 2006. - 536 pages.
Hyperbolic Partial Differential Equations(PDEs), and in particular first-order systems of conservation laws, have been a fashionable topic for over half a century. Many book shave been written, but few of them deal with genuinely multidimensional hyperbolic problems: in this respect the most classical, though not so well-known,...
Springer, 1969. — 154 p. The present book deals with the construction of solutions of linear partial differential equations by means of integral operators which transform analytic functions of a complex variable into such solutions. The theory of analytic functions has achieved a high degree of development and simplicity, and the operator method permits us to exploit thi s theory...
Wiley, 2010. — 318 pages. The importance of partial differential equations (PDEs) in modeling phenomena in engineering as well as in the physical, natural, and social sciences is well known by students and practitioners in these fields. Striking a balance between theory and applications, Fourier Series and Numerical Methods for Partial Differential Equations presents an...
Germany: Springer, Centre de Recerca Matemàtica (CRM), 2009. — 208 p. — (Advanced Courses in Mathematics CRM Barcelona). — ISBN: 978-3-7643-8939-0. This book contains an expanded and smoothed version of lecture notes delivered by the authors at the Advanced School on Numerical Solutions of Partial Di - ential Equations. Wavelets and Partial Differential Equations...
Springer, 2007. — 283 p. This book introduces the treatment of linear and nonlinear (quasi-linear) abstract evolution equations by methods from the theory of strongly continuous semigroups. The theoretical part is accessible to graduate students with basic knowledge in functional analysis, with only some examples requiring more specialized knowledge from the spectral theory of...
De Gruyter, 2019. — 238 p. — (Nonlinear Analysis and Applications, 31). — ISBN: 978-3-11-062179-2. Extending the well-known connection between classical linear potential theory and probability theory (through the interplay between harmonic functions and martingales) to the nonlinear case of tug-of-war games and their related partial differential equations, this unique book...
Routledge, 1961. — 98 p. The book is an introduction both to Laplace's equation and its solutions and to a general method of treating partial differential equations. Chapter 1 discusses vector fields and shows how Laplace's equation arises for steady fields which are irrotational and solenoidal. In the second chapter the method of separation of variables is introduced and used...
New York: Chapman & Hall, 2017. — 766 p. Methods of solution for partial differential equations (PDEs) used in mathematics, science, and engineering are clarified in this self-contained source. The reader will learn how to use PDEs to predict system behaviour from an initial state of the system and from external influences, and enhance the success of endeavours involving...
New York: Springer, 2010. — 398 p. — ISBN: 978-0-387-98612-8 e-ISBN: 978-0-387-68028-6. Local Transformations and Conservation Laws Local Transformations Conservation Laws Noether's Theorem Some Connections Between Symmetries and Conservation Laws Construction of Mappings Relating Differential Equations Notations; Mappings of Infinitesimal Generators Mapping of a Given PDE to a...
Walter de Gruyter GmbH, Berlin/Boston, Germany, 2014. — 205 p. — (De Gruyter Studies in Mathematics 55) — ISBN: 978-3-11-031540-0. Elliptic partial differential equations is one of the main and most active areas in mathematics. In our book we study linear and nonlinear elliptic problems in divergence form, with the aim of providing classical results, as well as more recent...
North-Holland, 2020. — 692 p. — (Handbook of Numerical Analysis, Vol. 21). — ISBN: 978-0-444-64003-1, 978-0-444-64004-8. True PDF Besides their intrinsic mathematical interest, geometric partial differential equations (PDEs) are ubiquitous in many scientific, engineering and industrial applications. They represent an intellectual challenge and have received a great deal of...
New York: Springer, 2019. — 260 p. This book covers a diverse range of topics in Mathematical Physics, linear and nonlinear PDEs. Though the text reflects the classical theory, the main emphasis is on introducing readers to the latest developments based on the notions of weak solutions and Sobolev spaces. In numerous problems, the student is asked to prove a given statement, e.g....
Basel: Birkhäuser, 2010. — 231 p. The goal of this book is to investigate the behavior of weak solutions of the elliptic transmission problem in a neighborhood of boundary singularities: angular and conic points or edges. This problem is discussed for both linear and quasilinear equations. A principal new feature of this book is the consideration of our estimates of weak...
Elsevier, 2006. — 539 p. Introduction Preliminaries Integral inequalities The laplace operator Strong solutions of the Dirichlet problem for linear equations The Dirichlet problem for elliptic linear divergent equations in a nonsmooth domain The Dirichlet problem for semilinear equations in a conical domain Strong solutions of the Dirichlet problem for nondivergence quasilinear...
Springer, 2016. — 291 p. — (Universitext). — ISBN: 3319489348. This modern take on partial differential equations does not require knowledge beyond vector calculus and linear algebra. The author focuses on the most important classical partial differential equations, including conservation equations and their characteristics, the wave equation, the heat equation, function...
Birkhäusеr, Bоston, 2006. — 329 pages. This collection of original articles and surveys treats linear and nonlinear aspects of the theory of partial differential equations. Phase space analysis methods, also known as microlocal analysis, have yielded striking results over the past years and have become one of the main tools of investigation. Equally important is their role in...
Boca Raton: CRC Press, 2024. — 243 p. Linear Partial Differential and Difference Equations and Simultaneous Systems: With Constant or Homogeneous Coefficients is part of the series "Mathematics and Physics for Science and Technology," which combines rigorous mathematics with general physical principles to model practical engineering systems with a detailed derivation and...
Cambridge: Cambridge University Press, 2016. — 203 p. The area of nonlinear dispersive partial differential equations (PDEs) is a fast developing field which has become exceedingly technical in recent years. with this book, the authors provide a self-contained and accessible introduction for graduate or advanced undergraduate students in mathematics, engineering, and the physical...
Springer, 2018. — xi+198 p. — (Lecture Notes in Mathematics, 2220). — ISBN: 978-3-319-95186-7. The aim of this book is to present different aspects of the deep interplay between Partial Differential Equations and Geometry. It gives an overview of some of the themes of recent research in the field and their mutual links, describing the main underlying ideas, and providing...
Springer, 2012. - 158 pages. The book covers several topics of current interest in the field of nonlinear partial differential equations and their applications to the physics of continuous media and particle interactions. It treats the quasigeostrophic equation, integral diffusions, periodic Lorentz gas, Boltzmann equation, and critical dispersive nonlinear Schrödinger and wave...
CRC, 2005. - 304 Pages.
Separation of Variables for Partial Differential Equations: An Eigenfunction Approach includes many realistic applications beyond the usual model problems. The book concentrates on the method of separation of variables for partial differential equations, which remains an integral part of the training in applied mathematics. The presentation includes,...
Cambridge: Cambridge University Press, 2021. — 263 p. This introduction to the singularly perturbed methods in the nonlinear elliptic partial differential equations emphasises the existence and local uniqueness of solutions exhibiting concentration property. The authors avoid using sophisticated estimates and explain the main techniques by thoroughly investigating two...
Springer International Publishing, 2016 — 110p. — (SpringerBriefs in Mathematical Physics 12) — ISBN: 978-3-319-33370-0 (eBook), 978-3-319-33369-4 (Softcover). In this volume a theory for models of transport in the presence of a free boundary is developed.Macroscopic laws of transport are described by PDE's. When the system is open, there are several mechanisms to couple the...
Springer International Publishing AG, 2017. — 319 p. — (Applied and Numerical Harmonic Analysis) — ISBN: 9783319527413 This collection of articles and surveys is devoted to Harmonic Analysis, related Partial Differential Equations and Applications and in particular to the fields of research to which Richard L. Wheeden made profound contributions. The papers deal with Weighted...
North Holland, 1982. — 575 p. Since the fifties, the theory of partial differential equations has undergone considerable development , yet it is certainly one of those fields where we find both the largest number of research articles and the smallest number of works of synthesis. The specialist can come to terms with such a situation, but the student who desires an introduction...
Boca Raton: CRC Press, 2021. — 459 p. This book focusses on partial differential systems (PDS) from an engineering perspective covering robust stabilization control, filter, and reference tracking design in signal processing, control, and biological systems. Each of the chapter focuses on a specific design topic with deep investigation into the robust H∞ filtering,...
World Scientific Publishing, 2010. - 208 pages. ISBN: 9814304832
The book provides a comprehensive overview on the theory on analysis of singularities for partial differential equations. It contains a summarization of the formation, development and main results on this topic. Some of the author's discoveries and original contributions are also included, such as the propagation...
World Scientific Publishing Company, 2025. — 616 p. — ISBN-13: 978-9811298479. Over the past two decades, the method of fundamental solutions (MFS) has attracted great attention and has been used extensively for the solution of scientific and engineering problems. The MFS is a boundary meshless collocation method which has evolved from the boundary element method. In it, the...
Springer, 2019. — 455 p. — (Computational Methods in Applied Sciences 47). — ISBN: 3319783246. This book treats Modelling of CFD problems, Numerical tools for PDE, and Scientific Computing and Systems of ODE for Epidemiology, topics that are closely related to the scientific activities and interests of Prof. William Fitzgibbon, Prof. Yuri Kuznetsov, and Prof. O. Pironneau,...
Springer, 2024. — 322 p. Nonlinear partial differential equations (PDE) are at the core of mathematical modeling. In the past decades and recent years, multiple analytical methods to study various aspects of the mathematical structure of nonlinear PDEs have been developed. Those aspects include C- and S-integrability, Lagrangian and Hamiltonian formulations, equivalence...
Amsterdam: North Holland, 2007. — 627 p. List of Contributors Rearrangements and Applications to Symmetry Problems in PDE Liouville-Type Theorems for Elliptic Problems Similarity and Pseudosimilarity Solutions of Degenerate Boundary Layer Equations Monotonicity and Compactness Methods for Nonlinear Variational Inequalities Stationary Navier—Stokes Flow in 2-D Channels Involving...
Amsterdam: North Holland, 2006. — 617 p. List of Contributors Contents of Volume I Contents of Volume II Contents of Volume III Contents of Volume IV Semilinear Elliptic Systems: Existence, Multiplicity, Symmetry of Solutions Nonlinear Variational Problems via the Fibering Method Superlinear Elliptic Equations and Systems Nonlinear Eigenvalue Problem with Quantization...
Birkhäuser, 2009. — 289 p. — (Birkhäuser Advanced Texts). — ISBN: 9783764399818. The aim of this book is to introduce the reader to different topics of the theory of elliptic partial differential equations by avoiding technicalities and refinements. Apart from the basic theory of equations in divergence form it includes subjects such as singular perturbation problems,...
2nd ed. — Birkhäuser, 2024. — 392 p. — (Birkhäuser Advanced Texts Basler Lehrbücher). — ISBN 3031541219. The aim of this book is to introduce the reader to different topics of the theory of elliptic partial differential equations by avoiding technicalities and complicated refinements. Apart from the basic theory of equations in divergence form , it includes subjects as singular...
Amsterdam: North Holland, 2004. — 736 p. List of Contributors Solutions of Quasilinear Second-Order Elliptic Boundary Value Problems via Degree Theory Stationary Navier–Stokes Problem in a Two-Dimensional Exterior Domain Qualitative Properties of Solutions to Elliptic Problems On Some Basic Aspects of the Relationship between the Calculus of Variations and Differential...
Elsevier, 2005. — 625 p. — ISBN: 0444520457 A collection of self contained, state-of-the-art surveys. The authors have made an effort to achieve readability for mathematicians and scientists from other fields, for this series of handbooks to be a new reference for research, learning and teaching. Partial differential equations represent one of the most rapidly developing topics...
North Holland, 2006. — 630 p. This handbook is volume III in a series devoted to stationary partial differential quations. Similarly as volumes I and II, it is a collection of self contained state-of-the-art surveys written by well known experts in the field. The topics covered by this handbook include singular and higher order equations, problems near critically, problems with...
WSPC, 2024. — 283 p. Review of the First Edition: "The monograph is well written and organized and recommended to graduate students and researchers in applied mathematics or engineering." Zentralblatt MATH The primary focus of the book is to explore the asymptotic behavior of problems formulated within cylindrical structures. Various physical applications are discussed, with...
American Mathematical Society, 2022. — 647 p. — (Pure and Applied Undergraduate Texts, 54). — ISBN 1470464918, 9781470464912. While partial differential equations (PDEs) are fundamental in mathematics and throughout the sciences, most undergraduate students are only exposed to PDEs through the method of separation of variations. This text is written for undergraduate students...
University Of Chicago Press, 2001. — 360 p. Alberto P. Calderón (1920-1998) was one of this century's leading mathematical analysts. His contributions, characterized by great originality and depth, have changed the way researchers approach and think about everything from harmonic analysis to partial differential equations and from signal processing to tomography. In addition,...
Birkhäuser Basel, 2009. - 352 pages.
This volume includes several invited lectures given at the International Workshop "Analysis, Partial Differential Equations and Applications", held at the Mathematical Department of Sapienza University of Rome, on the occasion of the 70th birthday of Vladimir G. Maz'ya, a renowned mathematician and one of the main experts in the field of...
Springer, 2014. — 431 p. This book collects papers mainly presented at the "International Conference on Partial Differential Equations: Theory, Control and Approximation" (May 28 to June 1, 2012 in Shanghai) in honor of the scientific legacy of the exceptional mathematician Jacques-Louis Lions. The contributors are leading experts from all over the world, including members of the...
Springer, 2021. — 467 p. The contributions contained in the volume, written by leading experts in their respective fields, are expanded versions of talks given at the INDAM Workshop "Anomalies in Partial Differential Equations" held in September 2019 at the Istituto Nazionale di Alta Matematica, Dipartimento di Matematica "Guido Castelnuovo", Università di Roma "La Sapienza"....
Springer, 2019. — 505 p. — (Series in Contemporary Mathematics 03). — ISBN: 981133031X. This is the first book on the subject of the periodic unfolding method (originally called "éclatement périodique" in French), which was originally developed to clarify and simplify many questions arising in the homogenization of PDE's. It has since led to the solution of some open problems....
Singapore: World Scientific Publishing Company, 2017. — 301 p. — ISBN: 978-9813229174. The book extensively introduces classical and variational partial differential equations (PDEs) to graduate and post-graduate students in Mathematics. The topics, even the most delicate, are presented in a detailed way. The book consists of two parts which focus on second order linear PDEs....
Elsevier Science, 2002. — 665 p.
This volume is the 14 th and last one of the series "Nonlinear Partial Differential Equations and their Applications. Coll~ge de France Seminar", which published the texts of the lectures given at the seminars organized by Jacques-Louis Lions, from his election at the Coll~ge de France in 1973 until
his retirement in 1998. It was one of the...
Springer Nature Singapore, 2024. — 153 p. This book are notes prepared for the PhD courses that the author has been teaching during the last 10 years. The material available in the already existing literature (papers and essays) has been collected in this unique text, presenting the results with all the details for the reader’s convenience, fixing a unified notation, and...
3rd ed. — CRC Press, 2024. — 509 p. — (Advances in Applied Mathematics). — ISBN 1032639385. The first two editions of An Introduction to Partial Differential Equations with MatLAB gained popularity among instructors and students at various universities throughout the world . Plain mathematical language is used in a friendly manner to provide a basic introduction to partial...
Second Edition. — CRC Press, 2013. — 654 p. An Introduction to Partial Differential Equations with MatLAB, Second Edition illustrates the usefulness of PDEs through numerous applications and helps students appreciate the beauty of the underlying mathematics. Updated throughout, this second edition of a bestseller shows students how PDEs can model diverse problems, including the...
Springer International Publishing AG, 2017. — 398 p. — (Trends in Mathematics) — ISBN: 978-3-319-62361-0. Daniel Alpay graduated in 1986 from the Weizmann Institute of Science with the Ph.D. thesis: “Reproducing kernel Krein spaces of analytic functions and inverse scattering” under the supervision of Prof. Harry Dym. After graduating, he occupied positions at the University of...
London: Pitman Publishing, 1976. — 148 p. — ISBN: 0-273-00307-0. These lecture notes are intended to be a companion volume to D. Colton, Partial Differential Equations in the Complex Domain, Pitman Press Lecture Note Series, London, 1976. In that book a general survey was given of the analytic theory of partial differential equations, with particular emphasis on improperly...
4th ed. — Boca Raton: CRC Press, 2022. — 440 p. — ISBN 1032001666. Solution Techniques for Elementary Partial Differential Equations, Fourth Edition remains a top choice for a standard, undergraduate-level course on partial differential equations (PDEs). It provides a streamlined, direct approach to developing student’s competence in solving PDEs, and offers concise, easily...
Springer Science+Business Media, 1998. — 541 Pages. ISBN: 1461272661 The subject of partial differential equations has an unchanging core of material but is constantly expanding and evolving. Introduction to Partial Differential Equations with MatLAB is a careful integration of traditional core topics with modern topics, taking full advantage of the computational power of...
2nd ed. — Springer, 2025. — 267 p. — (Synthesis Lectures on Mathematics & Statistics). — ISBN 3031599748. This book provides a concise but thorough introduction to partial differential equations which model phenomena that vary in both space and time. The author begins with a full explanation of the fundamental linear partial differential equations of physics . The text...
New York: Morgan & Claypool, 2021. — 234 p. Condensed Summary by Chapter: Review the definitions of the divergence, gradient, and curl in three spatial dimensions.Use Green’s, Stokes’, and Gauss’s Divergence Theorem to help establish Faraday’s Law, Coulomb’s Law, and Ampere’s Law. Use these results to present Maxwell’s equations. This is the starting point for the book’s...
New York: Dover Publications, 2012. — 661 p. I have designed this book as a course for senior year or first-year graduate students in mathematics and mathematically-oriented beginning graduate students in engineering and the applied sciences. Its aim is to fill the gap between elementary textbooks that deal almost exclusively with separation of variables and integral transform...
Global Media, 2009. - 124 pages
Introduction to Partial Differential Equations This book is intended as a Partial Differential Equations reference for individuals who already posses a firm understanding of ordinary differential equations and at least have a basic idea of what a partial derivative is. This book is meant to be easily readable to engineers and scientists while still...
New York: Springer, 2004. — 333 p. This volume contains a slected number of articles based on lectures delivered at the IMA 2001 Summer Program on Geometric Methods in Inverse Problems and PDE Control. This program was focused on a set of common tools that are used in the study of inverse coefficient problems and control problems for partial differential equations, and in...
Marcel Dekker Inc., 2005. — 360 p. — (Lecture Notes in Pure and Applied Mathematics 245). — ISBN 10 0824700279. — ISBN 13 978-0824700270. Stochastic Partial Differential Equations and Applications gives an overview of current state-of-the-art stochastic PDEs in several fields, such as filtering theory, stochastic quantization, quantum probability, and mathematical finance....
Cambridge: Cambridge University Press, 2002. — 397 p. Second order linear parabolic and elliptic equations arise frequently in mathematical physics, biology and finance. Here the authors present a state of the art treatment of the subject from a new perspective. They then go on to discuss how the results in the book can be applied to control theory. This area is developing rapidly...
Springer, 2019. — 392 p. — (Trends in Mathematics). — ISBN: 978-3-030-10936-3. This book features a collection of papers devoted to recent results in nonlinear partial differential equations and applications. It presents an excellent source of information on the state-of-the-art, new methods, and trends in this topic and related areas. Most of the contributors presented their...
Springer Science+Business Media, 1999. — 277 p. — ISBN: 0817641211
Nonlinear partial differential equations has become one of the main tools of mod ern mathematical analysis; in spite of seemingly contradictory terminology, the subject of nonlinear differential equations finds its origins in the theory of linear differential equations, and a large part of functional analysis...
North Holland, 2008. — 608 р.
The material collected in this volume discusses the present as well as expected future directions of development of the field with particular emphasis on applications. The seven survey articles present different topics in Evolutionary PDE's, written by leading experts. Review of new results in the area.
Springer, 1992. — 226 p. In recent years there has been a great deal of activity in both the theoretical and applied aspects of partial differential equations, with emphasis on realistic engineering applications, which usually involve lack of smoothness. On March 21-25, 1990, the University of Chicago hosted a workshop that brought together approximately fortyfive experts in...
N.-Y.: Springer, 2009. — 230 p.
In May 2006, The University of Utah hosted an NSF-funded minicourse on stochastic partial differential equations. The goal of this minicourse was to introduce graduate students and recent Ph.D.s to various modern topics in stochastic PDEs, and to bring together several experts whose research is centered on the interface between Gaussian analysis,...
Paris: Société Mathématique de France, 2023. — 152 p. Motivation and a general overview of the main results Motivation Additional historical comments A rough outline of the main assumptions and results Our assumptions Some examples where our assumptions hold Classical elliptic operators Ahlfors regular sets Caffarelli and Sylvestre fractional operators Sawtooth domains Balls...
W. H. Freeman, 2012. — 335 p. — ISBN: 1429275928, 9781429275927. Drawing on his decade of experience teaching the differential equations course, John Davis offers a refreshing and effective new approach to partial differential equations that is equal parts computational proficiency, visualization, and physical interpretation of the problem at hand.
Springer, 2014. — 465 p. — (Progress in Nonlinear Differential Equations and Their Applications 85). — ISBN: 978-3-319-04213-8. This volume is a collection of articles presented at the Workshop for Nonlinear Analysis held in João Pessoa, Brazil, in September 2012. The influence of Bernhard Ruf, to whom this volume is dedicated on the occasion of his 60th birthday, is...
Birkhäuser Boston, 2011. — 883 p. The revised and enlarged third edition of this successful book presents a comprehensive and systematic treatment of linear and nonlinear partial differential equations and their varied and updated applications. In an effort to make the book more useful for a diverse readership, updated modern examples of applications are chosen from areas of...
American Mathematical Society, 2015. — 92 p. — (Memoirs of the American Mathematical Society v.234, №1103) — ISBN: 1470409836. The Hamiltonian defined on functions on $\mathbb{R}\times X$, where $X$ is a compact manifold, has critical points which are solutions of the linear Klein-Gordon equation. The author considers perturbations of this Hamiltonian, given by polynomial...
Springer, 2012. - 483 Pages. The theory of elliptic boundary problems is fundamental in analysis and the role of spaces of weakly differentiable functions (also called Sobolev spaces) is essential in this theory as a tool for analysing the regularity of the solutions. This book offers on the one hand a complete theory of Sobolev spaces, which are of fundamental importance for...
Springer Basel AG, 2011. - 355 pages. Operator Theory: Advances and Applications. Vol. 211
This volume collects six articles on selected topics at the frontier between partial differential equations and spectral theory, written by leading specialists in their respective field. The articles focus on topics that are in the center of attention of current research, with original...
McGraw-Hill, 1968. — 382 p. — ISBN: 9780070163966, 0070163960. Partial Differential Equations presents a balanced and comprehensive introduction to the concepts and techniques required to solve problems containing unknown functions of multiple variables. While focusing on the three most classical partial differential equations (PDEs)—the wave, heat, and Laplace equations—this...
Springer, 1987. — 174 p. Let me begin by explaining the meaning of the title of this book. In essence, the book studies boundary value problems for linear partial differ ential equations in a finite domain in n-dimensional Euclidean space. The problem that is investigated is the question of the dependence of the nature of the solvability of a given equation on the way in which...
Springer, 2018. — 199 p. — ISBN: 978-3-030-00448-4. This book, which is a continuation of Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces, presents recent trends and developments upon fractional, first, and second order semilinear difference and differential equations, including degenerate ones. Various stability, uniqueness, and existence results...
Springer, 1993. - 402 pages. Mathematicians have only recently begun to understand the local structure of solutions of degenerate and singular parabolic partial differential equations. The problem originated in the mid '60s with the work of DeGiorgi, Moser, Ladyzenskajia and Uraltzeva. This book will be an account of the developments in this field over the past five years. It...
2nd ed. — Birkhäuser, 2010. — 403 p. — ISBN: 978-0-8176-4551-9. This text is meant to be a self-contained, elementary introduction to Partial Differential Equations, assuming only advanced differential calculus and some basic LP theory. Although the basic equations treated in this book, given its scope, are linear, we have made an attempt to approach them from a nonlinear...
Cham: Birkhäuser, 2023. — 768 p. This graduate textbook provides a self-contained introduction to the classical theory of partial differential equations (PDEs). Through its careful selection of topics and engaging tone, readers will also learn how PDEs connect to cutting-edge research and the modeling of physical phenomena. The scope of the Third Edition greatly expands on that...
Singapore: World Scientific Publishing Company, 2024. - 669 p. - ISBN 9811291624. This is a textbook that covers several selected topics in the theory of elliptic partial differential equations which can be used in an advanced undergraduate or graduate course . The book considers many important issues such as existence, regularity, qualitative properties, and all the classical...
Berlin: de Gruyter, 2020. — 310 p. Acknowledgment Introduction Preliminary concepts Solvability of the abstract Cauchy problem Global in time continuation of solutions Definitions, properties, estimates, and inequalities Navier–Stokes equation in 2D and 3D N-D Navier–Stokes equation, an extended discussion Cauchy’s problem for 2-D quasi-geostrophic equation Dirichlet’s problem...
Walter de Gruyter, 2007. - 245 pages.
This textbook presents a first introduction to PDEs on an elementary level, enabling the reader to understand what partial differential equations are, where they come from and how they can be solved. The intention is that the reader understands the basic principles which are valid for particular types of PDEs, and to acquire some classical...
2nd ed. — De Gruyter, 2014. — 291 p. — (de Gruyter Textbook). — ISBN: 311031665X, 9783110316650, e-ISBN: 9783110316674
This book presents a first introduction to PDEs on an elementary level, enabling the reader to understand what partial differential equations are, where they come from and how they can be solved. The intention is that the reader understands the basic principles...
Berlin: de Gruyter, 1997. — 232 p. The book is very well written and will be a valuable source for specialists in differential equations, functional analysis, operator theory, and mathematical physics, as well as for non-specialists who want to get an idea of this fascinating field of contemporary nonlinear analysis. The authors have achieved a double goal. On the one hand,...
Springer, 2019. — 131 p. — (SpringerBriefs in Mathematics). — ISBN: 978-3-030-27229-6. This monograph requires basic knowledge of the variational theory of elliptic PDE and the techniques used for the analysis of the Finite Element Method. However, all the tools for the analysis of FEM (scaling arguments, finite dimensional estimates in the reference configuration, Piola...
Oxford University Press, 2010. — 368 p. Most nonlinear differential equations arising in natural sciences admit chaotic behavior and cannot be solved analytically. Integrable systems lie on the other extreme. They possess regular, stable, and well behaved solutions known as solitons and instantons. These solutions play important roles in pure and applied mathematics as well as...
Berlin: de Gruyter, 2022. — 236 p. The introduction of cross diffusivity opens many questions in the theory of reactiondiffusion systems. This book will be the first to investigate such problems presenting new finddings for researchers interested in studying parabolic and elliptic systems where classical methods are not applicable. In addition, The Gagliardo-Nirenbergi...
New York: Chapman and Hall/CRC, 2011. - 335p.
Stable solutions are ubiquitous in differential equations. They represent meaningful solutions from a physical point of view and appear in many applications, including mathematical physics (combustion, phase transition theory) and geometry (minimal surfaces).
Stable Solutions of Elliptic Partial Differential Equations offers a...
Boca Raton: CRC Press, 2018. — 591 p. Editor's Preface The Author The Editor Basic Notation Modern formulations of elliptic boundary value problems Variational principles of mathematical physics Variational problems in a Hilbert space Completion of a preHilbert space and basic properties of Sobolev spaces Generalized solutions of elliptic boundary value problems Projective-grid...
Singapore: World Scientific, 1992. — 341 p. The purpose of the book is to provide research workers in applied mathematics, physics, and engineering with practical geometric methods for solving systems of nonlinear partial differential equations. The first two chapters provide an introduction to the more or less classical results of Lie dealing with symmetries and similarity...
Cham: Springer, 2018. — 273 p. This book deals with a systematic study of a dynamical system approach to investigate the symmetrization and stabilization properties of nonnegative solutions of nonlinear elliptic problems in asymptotically symmetric unbounded domains. The usage of infinite dimensional dynamical systems methods for elliptic problems in unbounded domains as well...
Springer, 1995. - 208 Pages. The book contains a survey of the modern theory of general linear partial differential equations and a detailed review of equations with constant coefficients. Readers will be interested in an introduction to microlocal analysis and its applications including singular integral operators, pseudodifferential operators, Fourier integral operators and...
Springer, 1998. — 265 p. From the reviews of the first printing, published as volume 30 of the Encyclopaedia of Mathematical Sciences: "... I think the volume is a great success and an excellent preparation for future volumes in the series... the introductory style of Egorov and Shubin is .. attractive... a welcome addition to the literature and I am looking forward to the...
Birkhauser, 2004. — 394 p. The theory of parabolic equations, a well-developed part of the contemporary partial differential equations and mathematical physics, is the subject theory of of an immense research activity. A continuing interest in parabolic equations is caused both by the depth and complexity of mathematical problems emerging here, and by its importance in specific...
Walter de Gruyter, 2009. - 290 pages. This text contains a series of self-contained reviews on the state of the art in different areas of partial differential equations, presented by French mathematicians. Topics include qualitative properties of reaction-diffusion equations, multiscale methods coupling atomistic and continuum mechanics, adaptive semi-Lagrangian schemes for the...
Robert E. Krieger Publishing Company, 1962. - 282p. Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the...
Springer International Publishing AG, 2017. — 261 p. — (Mathematical Engineering) — ISBN: 3319552112. This monograph presents a graduate-level treatment of partial differential equations (PDEs) for engineers. The book begins with a review of the geometrical interpretation of systems of ODEs, the appearance of PDEs in engineering is motivated by the general form of balance laws...
American Mathematical Society, 2011. — 410 p. his book is a reader-friendly, relatively short introduction to the modern theory of linear partial differential equations. An effort has been made to present complete proofs in an accessible and self-contained form. The first three chapters are on elementary distribution theory and Sobolev spaces with many examples and applications...
Providence: American Mathematical Society, 2015. — 210 p. This volume contains the proceedings of the Conference on Spectral Theory and Partial Differential Equations, held from June 17–21, 2013, at the University of California, Los Angeles, California, in honor of James Ralston's 70th Birthday. Papers in this volume cover important topics in spectral theory and partial...
UC Berkeley, Department of Mathematics. — 213 p. Overview. Themes. Entropy and equilibrium . Thermal systems in equilibrium. Examples. Simple fluids. Other examples. Physical interpretations of the model. Equilibrium. Positivity of temperature. Extensive and intensive parameters. Concavity of S. Convexity of E. Entropy maximization, energy minimization. Thermodynamic...
Lecture Notes. — The George Washington University Press, 2010. — 101 p. These lecture notes are intended to supplement a one-semester graduate-level engineering course at The George Washington University in numerical methods for the solution of partial differential equations. Both finite difference and finite element methods are included. The main prerequisite is a standard...
American Mathematical Society, 2017. — 330 p. — (Mathematical Surveys and Monographs 224). — ISBN: 1470437856. Partial dynamical systems, originally developed as a tool to study algebras of operators in Hilbert spaces, has recently become an important branch of algebra. Its most powerful results allow for understanding structural properties of algebras, both in the purely...
EMS Press, 2021. — 496 p. — (EMS Series of Congress Reports vol.18). — ISBN-13 9783985475070. This volume is dedicated to Ari Laptev on the occasion of his 70th birthday. It collects contributions by his numerous colleagues sharing with him research interests in analysis and spectral theory. In brief, the topics covered include Friedrichs, Hardy, and Lieb-Thirring inequalities,...
Dover, 1993. - 414 pages. This highly useful text for students and professionals working in the applied sciences shows how to formulate and solve partial differential equations. Realistic, practical coverage of diffusion-type problems, hyperbolic-type problems, elliptic-type problems and numerical and approximate methods. Suggestions for further reading. Solution guide...
European Mathematical Society, 2017. — 212 p. — (Zurich Lectures in Advanced Mathematics) — ISBN: 3037191708 The Monge-Ampère equation is one of the most important partial differential equations, appearing in many problems in analysis and geometry. This monograph is a comprehensive introduction to the existence and regularity theory of the Monge-Ampère equation and some...
Springer International Publishing AGб 2018. — ix+216 p. — (Lecture Notes in Mathematics, 2211). — ISBN: 978-3-319-74042-3. This book collects together lectures by some of the leaders in the field of partial differential equations and geometric measure theory. It features a wide variety of research topics in which a crucial role is played by the interaction of fine analytic...
Arkansas Tech University, 2013. — 258 p. The Basics of the Theory of Partial Di_erential Equation. Review of Some ODE Results. First Order Partial Di_erential Equations. Second Order Linear Partial Di_erential Equations. The Laplace Transform Solutions for PDEs. The Fourier Transform Solutions for PDEs. Answers and Solutions.
Wadsworth Publishing Company, 1982. - 484 pages.
The same, refined Ordinary Differential Equations with Modern Applications by Finizio and Lades is the backbone of this text. In addition to this are included applications, techniques and theory of partial difference equations, difference equations and Fourier analysis.
This book is designed for an introductory, one-semester...
Springer, 2021. — 142 p. This volume covers contemporary aspects of geometric measure theory with a focus on applications to partial differential equations, free boundary problems and water waves. It is based on lectures given at the 2019 CIME summer school “Geometric Measure Theory and Applications – From Geometric Analysis to Free Boundary Problems” which took place in...
Phiadelphia: Society for Industrial and Applied Mathematics, 2008. — 352 p. This book presents a new approach to analyzing initial-boundary value problems for integrable partial differential equations (PDEs) in two dimensions, a method that the author first introduced in 1997 and which is based on ideas of the inverse scattering transform. This method is unique in also yielding...
Princeton University Press, 1995. - 352 Pages. ISBN: 0691043612 Second Edition The second edition of Introduction to Partial Differential Equations, which originally appeared in the Princeton series Mathematical Notes, serves as a text for mathematics students at the intermediate graduate level. The goal is to acquaint readers with the fundamental classical results of partial...
Cambridge: At the University Press, 1906. — 478 pages.
Introduction: two existence theorems.
Cauchy's theorem.
Linear equations and complete linear systems.
Non-linear equations.
Equations of the first order.
The method of characteristics for two independent variables.
Singular integrals.
The method of characteristics in any number of independent variables.
Lie's...
Springer, 2021. — 120 p. — (Springer Briefs in Mathematics). — ISBN 978-3030693480. This book collects some basic results on the null controllability for degenerate and singular parabolic problems. It aims to provide postgraduate students and senior researchers with a useful text, where they can find the desired statements and the related bibliography. For these reasons, the...
4th ed. — Springer, 1991. — 249 p. — (Applied Mathematical Sciences). — ISBN: 0387906096, 9780387906096. Identifies significant aspects of the theory and explores them with a limited amount of machinery from mathematical analysis. This book contains a chapter on Lewy's example of a linear equation without solutions.
Springer, 2020. — 193 p. — (Mathématiques et Applications 84). — ISBN: 978-3-030-45043-4. This book provides a unified analysis and scheme for the existence and uniqueness of strong and mild solutions to certain fractional kinetic equations. This class of equations is characterized by the presence of a nonlinear time-dependent source, generally of arbitrary growth in the...
Chapman and Hall/CRC, 2004. — 376 p. Unlike the classical Sturm theorems on the zeros of solutions of second-order ODEs, Sturm's evolution zero set analysis for parabolic PDEs did not attract much attention in the 19th century, and, in fact, it was lost or forgotten for almost a century. Briefly revived by Pólya in the 1930's and rediscovered in part several times since, it was...
Chapman and Hall/CRC, 2006. - 528 p.
Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics is the first book to provide a systematic construction of exact solutions via linear invariant subspaces for nonlinear differential operators. Acting as a guide to nonlinear evolution equations and models from physics and mechanics,...
Birkhauser, 2004. — 377 p. — (Progress in Nonlinear Differential Equations and Their Applications Volume 56) — ISBN13: 978-1-4612-7396-7. This book introduces a new, state-of-the-art method for the study of the asymptotic behavior of solutions to evolution partial differential equations; much of the text is dedicated to the application of this method to a wide class of...
American Mathematical Society, 2018. — 90 p. — (Memoirs of the American Mathematical Society,Vol.253, №1210). — ISBN: 1470428407. The authors study noncompact surfaces evolving by mean curvature flow (mcf). For an open set of initial data that are C3-close to round, but without assuming rotational symmetry or positive mean curvature, the authors show that mcf solutions become...
Boca Raton, USA: CRC Press, Taylor & Francis Group, 2018 (First published 1995). — 336 p. — (Studies in Advanced Mathematics). — ISBN13: 978-1-315-89303-7. Fourier Analysis and Partial Differential Equations presents the proceedings of the conference held at Miraflores de la Sierra in June 1992. These conferences are held periodically to assess new developments and results in...
Springer, 2014. — 258 p. — ISBN: 3319105442 This volume of papers presented at the conference in honor of Calixto P. Calderón by his friends, colleagues, and students is intended to make the mathematical community aware of his important scholarly and research contributions in contemporary Harmonic Analysis and Mathematical Models applied to Biology and Medicine, and to...
Springer, 2024. — 423 p. — (Problem Books in Mathematics). — ISBN 3031487834. Presenting a rich collection of exercises on partial differential equations, this textbook equips readers with 96 examples, 222 exercises, and 289 problems complete with detailed solutions or hints. It explores a broad spectrum of partial differential equations, fundamental to mathematically oriented...
N.-Y: Springer, 2015. — 218 p.
This book explains many fundamental ideas on the theory of distributions. The theory of partial differential equations is one of the synthetic branches of analysis that combines ideas and methods from different fields of mathematics, ranging from functional analysis and harmonic analysis to differential geometry and topology. This presents...
Boca Raton: CRC Press, 2023. - 268 p. - (Advances in Applied Mathematics). - ISBN 1032575034. This book presents an introduction to the theory of multiplicative partial differential equations (MPDEs) . It is suitable for all types of basic courses on MPDEs. The author’s aim is to present a clear and well-organized treatment of the concept behind the development of mathematics...
2nd edition. — Springer, 2021. — 270 p. — ISBN 978-3-030-81264-5. This book explains many fundamental ideas on the theory of distributions. The theory of partial differential equations is one of the synthetic branches of analysis that combines ideas and methods from different fields of mathematics, ranging from functional analysis and harmonic analysis to differential geometry...
Springer, 2020. — 319 p. — (Trends in Mathematics). — ISBN: 978-3-030-58214-2. This book originates from the session "Harmonic Analysis and Partial Differential Equations" held at the 12th ISAAC Congress in Aveiro, and provides a quick overview over recent advances in partial differential equations with a particular focus on the interplay between tools from harmonic analysis,...
Cambridge University Press, 2016. — 364 p. — ISBN10: 1107138388. — ISBN13: 978-1107138384 In this monograph, the authors present some powerful methods for dealing with singularities in elliptic and parabolic partial differential inequalities. Here, the authors take the unique approach of investigating differential inequalities rather than equations, the reason being that the...
Birkhäuser, 2010. — 294 p. — (Progress in Nonlinear Differential Equations and Their Applications 79). — ISBN: 978-0-8176-4651-6, 978-0-8176-4173-3.
The main focus of this textbook, in two parts, is on showing how self-similar solutions are useful in studying the behavior of solutions of nonlinear partial differential equations, especially those of parabolic type. The...
Basel: Birkhäuser, 2001. — 262 p. The purpose of this publication is to present, in one book, various approaches to analytic problems that arise in the context of singular spaces. It is based on the workshop 'Approaches to Singular Analysis' which was held on April 8-10, 1999, at Humboldt University of Berlin. The aim of this workshop was to bring together young mathematicians...
New York: Springer, 2001. — 532 pages. This is a book of interest to any having to work with differential equations, either as a reference or as a book to learn from. The authors have taken trouble to make the treatment self-contained. It is suitable required reading for a PhD student. Although the material has been developed from lectures at Stanford, it has developed into an...
Academic Press, 1969. - 306 Pages. ISBN: 0122830504 Volume 54 in Mathematics in Science and Engineering In traditional treatments of the partial differential equations of mathematical physics, particular stress is laid on solving boundary value problems and initial-boundary value problems. The reasons are that these problems were the natural ones to consider in classical...
2nd edition. — New York: Chapman and Hall/CRC, 2018. — 531 p. This book treats the Atiyah-Singer index theorem using the heat equation, which gives a local formula for the index of any elliptic complex. Heat equation methods are also used to discuss Lefschetz fixed point formulas, the Gauss-Bonnet theorem for a manifold with smooth boundary, and the geometrical theorem for a...
Springer Science + Business Media B.V., 2008. - 294 pages.
For more than 250 years partial differential equations have been clearly the most important tool available to mankind in order to understand a large variety of phenomena, natural at first and then those originating from human activity and technological development. Mechanics, physics and their engineering applications...
Philadelphia: SIAM, 2002. - 614 pages. The book equally emphasizes classical and modern techniques of solution of partial differential equations. First of all it will be useful for acquaintance of students with new approaches based on the application of such software packages as Mathematica, MatLAB or Maple.
Philadelphia: SIAM, 2011. — 666 p. Partial differential equations (PDEs) are essential for modeling many physical phenomena. This undergraduate textbook introduces students to the topic with a unique approach that emphasizes the modern finite element method alongside the classical method of Fourier analysis. Additional features of this new edition include broader coverage of...
New York: Springer, 1996. — 519 p. Nonlinear hyperbolic systems in one space dimension Gas dynamics and reacting flows Finite difference schemes for one-dimensional systems The case of multidimensional systems An introduction to boundary conditions
Springer, 2014. — 321 p. Particle Systems and PDEs, Braga, Portugal, December 2012. This book presents the proceedings of the international conference Particle Systems and Partial Differential Equations I, which took place at the Centre of Mathematics of the University of Minho, Braga, Portugal, from the 5th to the 7th of December, 2012. The purpose of the conference was to bring...
Springer, 2015. — 395 p. Particle Systems and PDEs II, Braga, Portugal, December 2013. This book focuses on mathematical problems concerning different applications in physics, engineering, chemistry and biology. It covers topics ranging from interacting particle systems to partial differential equations (PDEs), statistical mechanics and dynamical systems. The purpose of the second...
Springer, 2016. — 352 p. Particle Systems and PDEs III, Braga, Portugal, December 2014. The main focus of this book is on different topics in probability theory, partial differential equations and kinetic theory, presenting some of the latest developments in these fields. It addresses mathematical problems concerning applications in physics, engineering, chemistry and biology...
Springer, 2017. — 309 p. PSPDE IV, Braga, Portugal, December 2015. "This book addresses mathematical problems motivated by various applications in physics, engineering, chemistry and biology. It gathers the lecture notes from the mini-course presented by Jean-Christophe Mourrat on the construction of the various stochastic “basic” terms involved in the formulation of the...
Cham: Springer Nature Switzerland, 2024. — 143 p. Introducing a groundbreaking framework for stochastic partial differential equations (SPDEs), this work presents three significant advancements over the traditional variational approach. Firstly, Stratonovich SPDEs are explicitly addressed. Widely used in physics, Stratonovich SPDEs have typically been converted to Ito form for...
European Mathematical Society, Zürich, Switzerland, 2014. — 172 p. — (EMS Series of Lectures in Mathematics 18). — ISBN13: 978-3037191316. The theme of this monograph is the nonlinear Schrödinger equation. This equation models slowly varying wave envelopes in dispersive media and arises in various physical systems such as water waves, plasma physics, solid state physics and...
Springer, 2003. — 471 p. Meshfree methods for the solution of partial differential equations gained much attention in recent years, not only in the engineering but also in the mathematics community. One of the reasons for this development is the fact that meshfree discretizations and particle models ar often better suited to cope with geometric changes of the domain of interest,...
Springer, 2005. — 306 p. The numerical treatment of partial differential equations with particle methods and meshfree discretization techniques is a very active research field both in the mathematics and engineering community. Due to their independence of a mesh, particle schemes and meshfree methods can deal with large geometric changes of the domain more easily than classical...
Springer, 2008. — 404 p. The numerical treatment of partial differential equations with particle methods and meshfree discretization techniques is a very active research field both in the mathematics and engineering community. Due to their independence of a mesh, particle schemes and meshfree methods can deal with large geometric changes of the domain more easily than classical...
Springer, 2013. — 243 p. Meshfree methods are a modern alternative to classical mesh-based discretization techniques such as finite differences or finite element methods. Especially in a time-dependent setting or in the treatment of problems with strongly singular solutions their independence of a mesh makes these methods highly attractive. This volume collects selected papers...
Springer, 2015. — 323 p. There have been substantial developments in meshfree methods, particle methods, and generalized finite element methods since the mid 1990s. The growing interest in these methods is in part due to the fact that they offer extremely flexible numerical tools and can be interpreted in a number of ways. For instance, meshfree methods can be viewed as a natural...
Springer, 2017. — 245 p. There have been substantial developments in meshfree methods, particle methods, and generalized finite element methods since the mid 1990s. The growing interest in these methods is in part due to the fact that they offer extremely flexible numerical tools and can be interpreted in a number of ways. For instance, meshfree methods can be viewed as a natural...
N.-Y.: Springer, 2015. - 368p.
This volume provides an introduction to the analytical and numerical aspects of partial differential equations (PDEs). It unifies an analytical and computational approach for these; the qualitative behaviour of solutions being established using classical concepts: maximum principles and energy methods.
Notable inclusions are the treatment of...
World Scientific, 2000. — 224 p. The inverse problem of the calculus of variations was first studied by Helmholtz in 1887 and it is entirely solved for the differential operators, but only a few results are known in the more general case of differential equations. This book looks at second-order differential equations and asks if they can be written as Euler–Lagrangian equations....
Department of Mathematics, University of California, Santa Barbara, 2010. - 96 pages. These lecture notes arose from the course "Partial Di erential Equations" - Math 124A taught by the author in the Department of Mathematics at UCSB in the fall quarters of 2009 and 2010. The selection of topics and the order in which they are introduced is based on Walter A. Strauss. Partial...
European Mathematical Society, 2017. — 498 p. — (EMS Tracts in Mathematics 26). — ISBN-13 9783037191675. Вырожденные комплексные уравнения Monge–Ampère Complex Monge–Ampère equations have been one of the most powerful tools in Kähler geometry since Aubin and Yau’s classical works, culminating in Yau’s solution to the Calabi conjecture. A notable application is the construction...
Singapore: World Scientific Publishing Co, 2015. — 348 p.
This book aims to introduce some new trends and results on the study of the fractional differential equations, and to provide a good understanding of this field to beginners who are interested in this field, which is the authors' beautiful hope. This book describes theoretical and numerical aspects of the fractional...
New Delhi: Laxmi Publications Pvt Ltd, 2019. — 131 p. — ISBN: 9352741021. The present book on ‘‘Partial Differential Equations’’ has been written as a textbook according to the latest guidelines and syllabus in Mathematics issued by the U.G.C. for various universities. The text of the book has been prepared with the following salient features: The language of the book is simple...
Editors: Matthew J. Gursky, Ermanno Lanconelli, Andrea Malchiodi, Gabriella Tarantello, Xu-Jia Wang, Paul C. Yang, Sun-Yung Alice Chang, Antonio Ambrosetti. — Springer, 2009. — 273 p. — (Lecture Notes in Mathematics 1977). — ISBN: 978-3-642-01673-8; 978-3-642-01674-5. This volume contains lecture notes on some topics in geometric analysis, a growing mathematical subject which...
Dover, 1997. - 476 pages. ISBN: 0486612716 Excellent undergraduate/graduate-level introduction presents full introduction to the subject and to the Fourier series as related to applied mathematics, considers principal method of solving partial differential equations, examines 1st-order systems, computation methods, and much more. Over 600 problems and exercises, with answers...
2nd Edition. — Springer International Publishing, 2016. — 225 p. — (Progress in Nonlinear Differential Equations and Their Applications. Volume 89) — ISBN: 9783319433721 Now in its second edition, this monograph explores the Monge-Ampère equation and the latest advances in its study and applications. It provides an essentially self-contained systematic exposition of the theory...
N.-Y.: Springer, 2015 - 449p.
This book is a unique selection of work by world-class experts exploring the latest developments in Hamiltonian partial differential equations and their applications. Topics covered within are representative of the field’s wide scope, including KAM and normal form theories, perturbation and variational methods, integrable systems, stability of...
5th edition. — Pearson Education, 2012. — 784 p. — ISBN10: 0321797051 This book emphasizes the physical interpretation of mathematical solutions and introduces applied mathematics while presenting differential equations. Coverage includes Fourier series, orthogonal functions, boundary value problems, Green’s functions, and transform methods. This text is ideal for readers...
China Machine Press, 2003. — 769 p.
Emphasizing the physical interpretation of mathematical solutions, this book introduces applied mathematics while presenting partial differential equations. Topics addressed include heat equation, method of separation of variables, Fourier series, Sturm-Liouville eigenvalue problems, finite difference numerical methods for partial...
4th edition. — Prentice Hall, 87 p.
In this manual there are solutions to most of the starred exercises of "Applied Partial Differential Equations: with Fourier Series and Boundary Value Problems", by Richard Haberman.
Over 1000 exercises of varying difficulty form an essential part of this text. It is hoped that these approximately 250 selected solutions will toe useful for...
Springer-Verlag, Berlin, 2003, 311 pages. The book offers a simultaneous presentation of the theory and of the numerical treatment of elliptic problems. The author starts with a discussion of the Laplace equation in the classical formulation and its discretisation by finite differences and deals with topics of gradually increasing complexity in the following chapters. He...
2nd Edition. — Springer, 2017. — 465 p. — (Springer Series in Computational Mathematics 18). — ISBN: 978-3-662-54960-5. This book simultaneously presents the theory and the numerical treatment of elliptic boundary value problems, since an understanding of the theory is necessary for the numerical analysis of the discretisation. It first discusses the Laplace equation and its...
American Mathematical Society, 2011. — 305 p. — (Graduate Studies in Mathematics 120). — ISBN-13 9780821852552. This is a textbook for an introductory graduate course on partial differential equations. Han focuses on linear equations of first and second order. An important feature of his treatment is that the majority of the techniques are applicable more generally. In...
European Mathematical Society, 2007. — 305 p. — (EMS Textbooks in Mathematics) — ISBN: 3037190426 It is the main aim of this book to develop at an accessible, moderate level an L*2* theory for elliptic differential operators of second order on bounded smooth domains in Euclidean n-space, including a priori estimates for boundary-value problems in terms of (fractional) Sobolev...
European Mathematical Society, 2014. — 301 p. — (Zurich Lectures in Advanced Mathematics 20). — ISBN 978-3-03719-134-7. Компактность и устойчивость нелинейных эллиптических уравнений The book offers an expanded version of lectures given at ETH Zürich in the framework of a Nachdiplomvorlesung. Compactness and stability for nonlinear elliptic equations in the inhomogeneous...
Boca Raton: CRC Press, 2019. — 395 p. — (Textbooks in Mathematics). — ISBN: 1138339830. Partial Differential Equations: Analytical Methods and Applications covers all the basic topics of a Partial Differential Equations (PDE) course for undergraduate students or a beginners’ course for graduate students. It provides qualitative physical explanation of mathematical results while...
Cambridge University Press, 2005. — 216 p. — (London Mathematical Society Lecture Note Series 318) — ISBN: 0521574919 Perturbation of the boundary is a rather neglected topic in the study of PDEs for two main reasons. First, on the surface it appears trivial, merely a change of variables and an application of the chain rule. Second, carrying out such a change of variables...
Springer, 1981. — 352 p. — (Lecture Notes in Mathematics 840). — ISBN: 978-3-540-10557-2, 978-3-540-38528-8. Preliminaries Examples of nonlinear parabolic equations in physical, biological and engineering problems Existence, uniqueness and continuous dependence Dynamical systems and liapunov stability Neighborhood of an equilibrium point Invariant manifolds near an equilibrium...
Cambridge: CUP, 2007.- 285p.
Spectral methods are well-suited to solve problems modeled by time-dependent partial differential equations: they are fast, efficient and accurate and widely used by mathematicians and practitioners. This class-tested introduction, the first on the subject, is ideal for graduate courses, or self-study. The authors describe the basic theory of...
Cambridge: Cambridge University Press, 2007. — 281 p. Spectral methods are well-suited to solve problems modeled by time-dependent partial differential equations: they are fast, efficient and accurate and widely used by mathematicians and practitioners. This class-tested introduction, the first on the subject, is ideal for graduate courses, or self-study. The authors describe...
Berlin: Springer, 2011. - 530p. The book contains a selection of high quality papers, chosen among the best presentations during the International Conference on Spectral and High-Order Methods (2009), and provides an overview of the depth and breadth of the activities within this important research area. The carefully reviewed selection of the papers will provide the reader...
Springer International Publishing AG, Switzerland, 2016. – 139 p. – ISBN10: 3319224697 The first book to introduce certified reduced basis methods for parametrized partial differentiation equations Unique focus on both the mathematical aspects and algorithmic elements of the methods Essential examples provide a point of departure for the development of more advanced...
Springer, 2016. — 139 p. During the past decade, reduced order modeling has attracted growing interest in computational science and engineering. It now plays an important role in delivering high-performance computing (and bridging applications) across industrial domains, from mechanical to electronic engineering, and in the basic and applied sciences, including neurosciences,...
N.-Y.: Wiley, 2012. - 696p. Uniquely provides fully solved problems for linear partial differential equations and boundary value problems Partial Differential Equations: Theory and Completely Solved Problems utilizes real-world physical models alongside essential theoretical concepts. With extensive examples, the book guides readers through the use of Partial Differential...
Springer International Publishing AG, 2018. — xxiii+444 p. — (Applied Mathematical Sciences, 199). — ISBN: 978-3-319-76895-3. This is a monograph on the emerging branch of mathematical biophysics combining asymptotic analysis with numerical and stochastic methods to analyze partial differential equations arising in biological and physical sciences. In more detail, the book...
N.-Y.: Springer, 2010. - 311p.
The first edition of Stochastic Partial Differential Equations: A Modeling, White Noise Functional Approach, gave a comprehensive introduction to SPDEs. In this, the second edition, the authors build on the theory of SPDEs driven by space-time Brownian motion, or more generally, space-time Lévy process noise. Applications of the theory are...
Springer-Verlag Berlin Heidelberg 2011. — (Applied Mathematical Sciences 152). — 362 pp. — ISBN: 978-3-642-23910-6 (Print) 978-3-642-23911-3 (Online). Hyperbolic conservation laws are central in the theory of nonlinear partial differential equations and in science and technology. The reader is given a self-contained presentation using front tracking, which is also a numerical...
Springer, 1997. — 301 p. — (Mathématiques et Applications). — ISBN10: 3540629211, ISBN13: 978-3540629214. In this introductory textbook, a revised and extended version of well-known lectures by L. H?rmander from 1986, four chapters are devoted to weak solutions of systems of conservation laws. Apart from that the book only studies classical solutions. Two chapters concern the...
Springer, 2011. — 145 p. There is an enormous amount of work in the literature about the blow-up behavior of evolution equations. It is our intention to introduce the theory by emphasizing the methods while seeking to avoid massive technical computations. To reach this goal, we use the simplest equation to illustrate the methods; these methods very often apply to more general...
Chapman and Hall/CRC, 2005. — 417 p. The field of control theory in PDEs has broadened considerably as more realistic models have been introduced and investigated. This book presents a broad range of recent developments, new discoveries, and mathematical tools in the field. The authors discuss topics such as elasticity, thermo-elasticity, aero-elasticity, interactions between...
UK: Cambridge University Press, 2001. — 417 p. — (Cambridge Studies in Advanced Mathematics 70). — ISBN-0-521-62116-X. This modern introduction to Fourier analysis and partial differential equations is intended to be used with courses for beginning graduate students. With minimal prerequisites the authors take the reader from fundamentals to research topics in the area of...
3rd Edition. — Springer International Publishing AG, 2017. — 414 p. — (Applied Mathematical Sciences 127) — ISBN: 3319516574 This book describes the contemporary state of the theory and some numerical aspects of inverse problems in partial differential equations. The topic is of substantial and growing interest for many scientists and engineers and accordingly to graduate...
Springer, 2006. — 358 p.
The topic of the inverse problems is of substantial and rapidly growing interest for many scientists and engineers. The second edition covers most important recent developments in the field of inverse problems, describing theoretical and computational methods, and emphasizing new ideas and techniques. It also reflects new changes since the first edition,...
Boca Raton: CRC Press, 2020. — 97 p. Differential equations play a noticeable role in engineering, physics, economics, and other disciplines. They permit us to model changing forms in both mathematical and physical problems. These equations are precisely used when a deterministic relation containing some continuously varying quantities and their rates of change in space and/or...
Academic Press, 2002. — 394 p. — ISBN 978-0123822529, 0123822521. This book is written to meet the needs of undergraduates in applied mathematics, physics and engineering studying partial differential equations. Many books deal with partial differential equations, some at an elementary level and others at more advanced levels, so it is necessary that some justification should...
N.-Y.: SIAM, 2011. — 235 p.
This book presents a systematic theory of Taylor expansions of evolutionary-type stochastic partial differential equations (SPDEs). The authors show how Taylor expansions can be used to derive higher order numerical methods for SPDEs, with a focus on pathwise and strong convergence. In the case of multiplicative noise, the driving noise process is...
Springer International Publishing, Switzerland, 2016. — 515 p. — (Developments in Mathematics 36) — ISBN: 3319290231. This monograph contains an in-depth analysis of the dynamics given by a linear Hamiltonian system of general dimension with nonautonomous bounded and uniformly continuous coefficients, without other initial assumptions on time-recurrence. Particular attention is...
R.S. Johnson & Ventus Publishing ApS, 2012. — 156 p. — ISBN: 9788776819699. Most descriptions of physical systems, as used in physics, engineering and, above all, in applied mathematics, are in terms of partial differential equations. This text, presented in three parts, introduces all the main mathematical ideas that are needed for the construction of solutions. The material...
Second Edition. — Springer, 2007. — 356 p. This book is intended for students who wish to get an introduction to the theory of partial differential equations. The author focuses on elliptic equations and systematically develops the relevant existence schemes, always with a view towards nonlinear problems. These are maximum principle methods (particularly important for numerical...
Third Edition. — Springer, 2013. — 415 p. — ISBN: 978-1-4614-4808-2. This book offers an ideal graduate-level introduction to the theory of partial differential equations. The first part of the book describes the basic mathematical problems and structures associated with elliptic, parabolic, and hyperbolic partial differential equations, and explores the connections between...
Springer International Publishing AG, Switzerland, 2016. – 146 p. – ISBN10: 3319342185 This book presents a range of entropy methods for diffusive PDEs devised by many researchers in the course of the past few decades, which allow us to understand the qualitative behavior of solutions to diffusive equations (and Markov diffusion processes). Applications include the large-time...
New York: Springer, 2015. - 123p. The purpose of this book is to give a quick and elementary, yet rigorous, presentation of the rudiments of the so-called theory of Viscosity Solutions which applies to fully nonlinear 1st and 2nd order Partial Differential Equations (PDE). For such equations, particularly for 2nd order ones, solutions generally are non-smooth and standard...
Springer International Publishing AG, 2018. — 310 p. — (Mathematics for Industry 31) — ISBN: 3319679422. This book presents new developments in non-local mathematical modeling and mathematical analysis on the behavior of solutions with novel technical tools. Theoretical backgrounds in mechanics, thermo-dynamics, game theory, and theoretical biology are examined in details. It...
New York: Prentice Hall, 2002. — 530 p. This extremely readable book illustrates how mathematics applies directly to different fields of study. Focuses on problems that require physical to mathematical translations, by showing readers how equations have actual meaning in the real world. Covers fourier integrals, and transform methods, classical PDE problems, the Sturm-Liouville...
N.-Y.: Springer, 2000. - 637p. This volume contains a broad treatment of important partial differential equations, particularly emphasizing the analytical techniques. In each chapter the author raises various questions concerning the particular equations discussed therein, discusses different methods for tackling these equations, gives applications and examples, and concludes...
Wadsworth & Brooks/Cole Advanced Books & Software, 1990. — 547 p. — ISBN: 0534122167 This is a text for a two-semester or three-quarter sequence of courses in partial differential equations. It is assumed that the student has a good background in vector calculus and ordinary differential equations and has been introduced to such elementary aspects of partial differential...
Springer, 2017. — 235 p. This book presents a concise study of controllability theory of partial differential equations when they are equipped with actuators and/or sensors that are finite dimensional at every moment of time. Based on the author’s extensive research in the area of controllability theory, this monograph specifically focuses on the issues of controllability,...
Cambridge University Press, 2018. — 255 p. — (Encyclopedia of Mathematics and its Applications). — ISBN: 978-1-107-18882-2. Starting from physical motivations and leading to practical applications, this book provides an interdisciplinary perspective on the cutting edge of ultrametric pseudodifferential equations. It shows the ways in which these equations link different fields...
Boston: Birkhäuser, 2007. — xv+293 p. — (Progress in Nonlinear Differential Equations and Their Applications, Vol. 71). — ISBN: 978-0-8176-4637-0. Fuchsian reduction is a method for representing solutions of nonlinear PDEs near singularities. The technique has multiple applications including soliton theory, Einstein's equations and cosmology, stellar models, laser collapse,...
Springer International Publishing Switzerland, 2015 — 337 pp. — (Applied Mathematical Sciences 190). — ISBN: 978-3-319-11085-1 (Print) 978-3-319-11086-8 (Online). This book gives a concise introduction to the basic techniques needed for the theoretical analysis of the Maxwell Equations, and filters in an elegant way the essential parts, e.g., concerning the various function...
Department of Mathematics, Princeton University, 72 pages. Basic definitions and examples General Equations General Ideas Main Equations Regularity or Break-down Main Goals Great Open Problems in PDE
Nova Science Publishers, Inc. — 2022. — 364 p. — (Mathematics Research Developments). — ISBN 978-1-68507-727-3. The laws of nature are written in the language of partial differential equations. Therefore, these equations arise as models in virtually all branches of science and technology. Our goal in this book is to help you to understand what this vast subject is about. The...
Springer, 2021. — 267 p. — ISBN 9813348216. This volume features selected, original, and peer-reviewed papers on topics from a series of workshops on Nonlinear Partial Differential Equations for Future Applications that were held in 2017 at Tohoku University in Japan. The contributions address an abstract maximal regularity with applications to parabolic equations, stability,...
Springer Science+Business Media, LLC 2009. — 161 pages. ISBN: 1441910956
This concise book covers the classical tools of PDE theory used in today's science and engineering: characteristics, the wave propagation, the Fourier method, distributions, Sobolev spaces, fundamental solutions, and Green's functions. The approach is problem-oriented, giving the reader an opportunity to...
Elsevier Science Ltd., 2020. — 267 p. — ISBN: 978-0-12-819235-1. Small-scale continuum mechanics theories are powerful tools for modelling miniature structures. By solving the governing equations of structural motion, the physical behaviour of these systems such as static behaviour, vibration and instability can be studied. However, this approach leads to strongly nonlinear...
John Wiley & Sons Inc, 1988. - 410 pages.
This book is devoted to the development of complex function theoretic methods in partial differential equations and to the study of analytic behaviour of solutions. It presents basic facts of the subject and includes recent results, emphasizing the method of integral operators and the method of differential operators. The first chapter...
European Mathematical Society, 2006. — 103 p. — (Zurich Lectures in Advanced Mathematics 03). — ISBN 9783037190210. Случайно вынужденные нелинейные уравнения в частных производных и статистическая гидродинамика в двух измерениях пространства This book gives an account of recent achievements in the mathematical theory of two-dimensional turbulence, described by the 2D...
CRC Press, 1997. — 378 p. — ISBN: 0849378532 This book provides an accessible treatment of this demanding subject. The authors integrate the use of Mathematica throughout the book rather than just providing a few sample problems at the end of chapters. Although rich in the theory for developing underlying mathematical analysis, the text emphasizes the development of methods....
De Gruyter, 2019. — 264 p. — (Radon Series on Computational and Applied Mathematics, Volume 25). — ISBN: 978-3-11-054848-8. This volume provides an introduction to modern space-time discretization methods such as finite and boundary elements and isogeometric analysis for time-dependent initial-boundary value problems of parabolic and hyperbolic type. Particular focus is given...
2nd Edition. — Springer-Verlag, Berlin, Heidelberg, 2003. — 882 p. — (Texts in Computational Science and Engineering 1) — ISBN: 9783642628115 During the last decades there has been a tremendous advancement of computer hardware, numerical algorithms, and scientific software. Engineers and scientists are now equipped with tools that make it possible to explore real world...
AMS, 2006. — 230 pages. — ISBN: 0821835769
The theory of hyperbolic equations is a large subject, and its applications are many: fluid dynamics and aerodynamics, the theory of elasticity, optics, electromagnetic waves, direct and inverse scattering, and the general theory of relativity. This book is an introduction to most facets of the theory and is an ideal text for a...
American Mathematical Society, 2006. — 230 p. The theory of hyperbolic equations is a large subject, and its applications are many: fluid dynamics and aerodynamics, the theory of elasticity, optics, electromagnetic waves, direct and inverse scattering, and the general theory of relativity. The first seven chapters of this book, based on notes of lectures delivered at Stanford in...
De Gruyter, 2019. — 136 p. Introduction General context Operators with constant second-order term Equations in divergence form Extensions Bibliography Index
Springer, 2018. — 259 p. — (Universitext). — ISBN: 3319783890. This textbook presents the essential parts of the modern theory of nonlinear partial differential equations, including the calculus of variations. After a short review of results in real and functional analysis, the author introduces the main mathematical techniques for solving both semilinear and quasilinear...
Basel: Birkhauser, 2016. - 395p. Covers the whole spectrum of partial differential equations, from modeling, analysis, to numerical analysis with numerical illustrations Covers the major deterministic numerical methods used in scientific computing practice Mathematically self-contained This book is devoted to the study of partial differential equation problems both from the...
Basel: Birkhäuser, 2022. — 410 p. This monograph explores applications of Carleman estimates in the study of stabilization and controllability properties of partial differential equations, including the stabilization property of the damped wave equation and the null-controllability of the heat equation. All analysis is performed in the case of open sets in the Euclidean space;...
World Scientific, 2009. — 544 Pages.
This book presents the theory of diffusion-reaction equations starting from the Volterra-Lotka systems developed in the eighties for Dirichlet boundary conditions. It uses the analysis of applicable systems of partial differential equations as a starting point for studying upper-lower solutions, bifurcation, degree theory and other nonlinear...
World Scientific Publishing Co Pte Ltd, 2014 - 193 p. In this monograph, the interplay between geometry and partial differential equations (PDEs) is of particular interest. It gives a selfcontained introduction to research in the last decade concerning global problems in the theory of submanifolds, leading to some types of Monge-Amp#65533;re equations.From the methodical point of...
World Scientific Publishing, 2010. - 464 pages. ISBN10: 9814322881 This volume is composed of two parts: Mathematical and Numerical Analysis for Strongly Nonlinear Plasma Models and Exact Controllability and Observability for Quasilinear Hyperbolic Systems and Applications. It presents recent progress and results obtained in the domains related to both subjects without...
World Scientific, 2014. — 176 p. — ISBN: 9814616389 This volume is on initial-boundary value problems for parabolic partial differential equations of second order. It rewrites the problems as abstract Cauchy problems or evolution equations, and then solves them by the technique of elementary difference equations. Because of this, the volume assumes less background and provides...
New York: Springer, 2016. - 73 p. Provides concise though comprehensive overview on the topic This book will appeal to a wide readership, from graduate students to researchers Enriches understanding on the topic This BCAM SpringerBriefs is a treaty of the Infinity-Laplace Equation, which has inherited many features from the ordinary Laplace Equation, and is based on lectures by...
N.-Y.: Springer, 2015. - 266p.
This book provides an introduction to the theory of stochastic partial differential equations (SPDEs) of evolutionary type. SPDEs are one of the main research directions in probability theory with several wide ranging applications. Many types of dynamics with stochastic influence in nature or man-made complex systems can be modelled by such...
N.-Y.: Wiley. 2008. - 398p.
Praise for the First Edition: "This book is well conceived and well written. The author has succeeded in producing a text on nonlinear PDEs that is not only quite readable but also accessible to students from diverse backgrounds." —SIAM Review A practical introduction to nonlinear PDEs and their real–world applications Now in a Second Edition, this...
N.-Y.: Springer, 2015. - 304p.
This textbook is for the standard, one-semester, junior-senior course that often goes by the title "Elementary Partial Differential Equations" or "Boundary Value Problems". The audience consists of students in mathematics, engineering, and the sciences. The topics include derivations of some of the standard models of mathematical physics and...
2nd Edition. — Springer, 2004. — 221 p. — (Undergraduate Texts in Mathematics). — ISBN: 0387209352. This text is written for the standard, one-semester, undergraduate course in elementary partial differential equations. The topics include derivations of some of the standard equations of mathematical physics (including the heat equation, the wave equation, and Laplace's...
Springer International Publishing AG, 2017. — 517 p. — (Universitext) — ISBN: 3319586459. Taking readers with a basic knowledge of probability and real analysis to the frontiers of a very active research discipline, this textbook provides all the necessary background from functional analysis and the theory of PDEs. It covers the main types of equations (elliptic, hyperbolic and...
Academic Press, 2019. — 272 p. — (Mathematics in Science and Engineering). — ISBN: 978-0-12-816798-4. This book evaluates the potential applications of POD reduced-order numerical methods in increasing computational efficiency, decreasing calculating load and alleviating the accumulation of truncation error in the computational process. Introduces the foundations of...
Basel: Birkhauser, 2003. — 280 p. This volume contains research articles from the field of Nonlinear Differential Equations which result from the "Workshop on Nonlinear Analysis and Applications" held in Bergamo on July 9 to 13, 200l. This workshop was the third edition of a meeting which first took place in Campinas in 1996 and was founded in part upon scientific cooperation,...
Boca Raton: CRC Press, 2024. — 452 p. Preface About the authors Introduction Linear PDEs Separation of Variables Method Symmetric Differential Operators Fourier Analysis Eigenfunction Expansion Method Special Functions Cylindrical and Spherical BVPs Bibliography Subject Index Index of Capsule Biographies
CRC Press, 2024. - 451 p. - ISBN 1032662522. Boundary value problems play a significant role in modeling systems characterized by established conditions at their boundaries. On the other hand, initial value problems hold paramount importance in comprehending dynamic processes and foreseeing future behaviors. The fusion of these two types of problems yields profound insights...
Springer, 2017. — 261 p. — (Mathematical Engineering). — ISBN: 978-3-319-55211-8. This monograph presents a graduate-level treatment of partial differential equations (PDEs) for engineers. The book begins with a review of the geometrical interpretation of systems of ODEs, the appearance of PDEs in engineering is motivated by the general form of balance laws in continuum...
Berlin: de Gruyter, 2013. — 264 p. In the last 40 years semi-linear elliptic equations became a central subject of study in the theory of nonlinear partial differential equations. On the one hand, the interest in this area is of a theoretical nature, due to its deep relations to other branches of mathematics, especially linear and nonlinear harmonic analysis, dynamical systems,...
Springer, 2019. — 383 p. — ISBN: 3319906461. This book was written based on lectures and tutorials held for mathematics and computer science students. Supplementary notions were added to these notes in order to make the reader refer to the bibliography as little as possible. The present form of the book is due to the essential contributions of our published results. We divided...
Springer, 2006. — 206 pages.
This book presents selected topics in science and engineering from an applied-mathematics point of view. The described natural, socioeconomic, and engineering phenomena are modeled by partial differential equations that relate state variables such as mass, velocity, and energy to their spatial and temporal variations. Typically, these equations are...
Society for Industrial & Applied Mathematics, 2005. — 665 p. Partial differential equations (PDEs) are used to describe a large variety of physical phenomena, from fluid flow to electromagnetic fields, and are indispensable to such disparate fields as aircraft simulation and computer graphics. While most existing texts on PDEs deal with either analytical or numerical aspects of...
Paris: European Mathematical Society, 2018. — 443 p. The present book is a detailed exposition of the author and his collaborators’ work on boundedness, continuity, and differentiability properties of solutions to elliptic equations in general domains, that is, in domains that are not a priori restricted by assumptions such as “piecewise smoothness” or being a “Lipschitz...
Academic Press, 2016. — 466 p. Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods focuses on two popular deterministic methods for solving partial differential equations (PDEs), namely finite difference and finite volume methods. The solution of PDEs can be very challenging, depending on the type of equation, the number of...
Lecture Notes. - Department of Mathematics, Leipzig University, 2012. - 205 pages. Examples Equations from variational problems Exercises Equations of first order Linear equations Quasilinear equations Nonlinear equations in two variables Nonlinear equations in Rn Hamilton-Jacobi theory Exercises Classification Linear equations of second order Quasilinear equations of second...
Moscú: Mir, 1978. — 426 p. Se estudian problemas de contorno para las ecuaciones elípticas, así como el problema de Cauchy y problemas mixtos para las ecuaciones hiperbólicas y parabólicas de segundo orden. Es de amplio uso el concepto de soluciones generalizadas. Para leer el libro basta dominar las bases de las matemáticas en los límites del programa para los dos primeros...
Translated from the Russian by P.C. Sinha, Cand. Sc. — Moscow: Mir publishers, 1978. — 408 p. Introduction. Classification of equations. Formulation of some problems. The Lebesgue integral and some questions of functional analysis. Function spaces. Elliptic equations. Hyperbolic equations. Parabolic equations.
Springer, 2019. — 530 p. — (Fields Institute Communications 83). — ISBN: 978-1-4939-9805-0. This volume contains lectures and invited papers from the Focus Program on "Nonlinear Dispersive Partial Differential Equations and Inverse Scattering" held at the Fields Institute from July 31-August 18, 2017. The conference brought together researchers in completely integrable systems...
N.-Y.: Springer, 2013. - 460p. The theory of distributions constitutes an essential tool in the study of partial differential equations. This textbook would offer, in a concise, largely self-contained form, a rapid introduction to the theory of distributions and its applications to partial differential equations, including computing fundamental solutions for the most basic...
2nd Edition. — Springer, 2018. — 615 p. — (Universitext). — ISBN: 978-3-030-03295-1. The aim of this book is to offer, in a concise, rigorous, and largely self-contained manner, a rapid introduction to the theory of distributions and its applications to partial differential equations and harmonic analysis. The book is written in a format suitable for a graduate course spanning...
Berlin: de Gruyter, 2021. — 290 p. This authoritative book presents recent research results on nonlinear problems with lack of compactness. The topics covered include several nonlinear problems in the Euclidean setting as well as variational problems on manifolds. The combination of deep techniques in nonlinear analysis with applications to a variety of problems make this work...
Springer, 2020. — 359 p. — (Operator Theory Advances and Applications 283). — ISBN: 978-3-030-60483-7. Considering that the motion of strings with finitely many masses on them is described by difference equations, this book presents the spectral theory of such problems on finite graphs of strings. The direct problem of finding the eigenvalues as well as the inverse problem of...
Kendall/Hunt Publishing Company, 2003. — 164 p. Power Series. Symmetry and Orthogonality. Fourier Series. Partial Differential Equations. PDE’s in Higher Dimensions. Using Mathematica to solve differential equations.
Springer, 2019. — 222 p. — (Progress in Nonlinear Differential Equations and Their Applications PNLDE Subseries in Control 93). — ISBN: 978-3-030-11098-7. This monograph presents a technique, developed by the author, to design asymptotically exponentially stabilizing finite-dimensional boundary proportional-type feedback controllers for nonlinear parabolic-type equations. The...
Birkhauser, 2006. - 778 pages.
One of the most fundamental and active areas in mathematics, the theory of partial differential equations (PDEs) is essential in the modeling of natural phenomena. PDEs have a wide range of interesting and important applications in every branch of applied mathematics, physics, and engineering, including fluid dynamics, elasticity, and optics....
Springer, 2019. — 469 p. — (Springer Series in Computational Mathematics 53). — ISBN: 9811376689. Recently, various mathematical problems have been solved by computer-assisted proofs, among them the Kepler conjecture, the existence of chaos, the existence of the Lorenz attractor, the famous four-color problem, and more. In many cases, computer-assisted proofs have the...
Cambridge: Cambridge University Press, 2020. — xx, 356 p. — (Cambridge–IISc Series). — ISBN: 978-1-108-83980-8. Suitable for both senior undergraduate and graduate students, this is a self-contained book dealing with the classical theory of the partial differential equations through a modern approach; requiring minimal previous knowledge. It represents the solutions to three...
Cambridge: Cambridge University Press, 2020. — 376 p. — (Cambridge–IISc Series). — ISBN: 1108839800. Suitable for both senior undergraduate and graduate students , this is a self-contained book dealing with the classical theory of the partial differential equations through a modern approach ; requiring minimal previous knowledge. It represents the solutions to three important...
Boca Raton: Chapman & Hall/CRC, 2006. — 372 p. The analysis and topology of elliptic operators on manifolds with singularities are much more complicated than in the smooth case and require completely new mathematical notions and theories. While there has recently been much progress in the field, many of these results have remained scattered in journals and preprints. Starting...
Berlin: de Gruyter, 1994. — 536 p. Introduction Elliptic boundary value problems in domains with smooth boundary Elliptic boundary value problems Elliptic problems with a parameter Dirichlet and Neumann problems for the Laplace operator in plane domains with corner points at the boundary Generalized solutions of the Dirichlet and Neumann problems in domains with corner points....
New York: Springer, 2012. - 388 p.
Nečas’ book Direct Methods in the Theory of Elliptic Equations, published 1967 in French, has become a standard reference for the mathematical theory of linear elliptic equations and systems. This English edition presents Nečas’ work essentially in the form it was published in 1967. It gives a timeless and in some sense definitive treatment of...
Lecture Notes. — Monterey, California: Department of Mathematics Naval Postgraduate School, 2002. — 355 p. Introduction and Applications . Basic Concepts and Definitions. Applications. Conduction of Heat in a Rod. Boundary Conditions. A Vibrating String. Boundary Conditions. Diffusion in Three Dimensions. Classification and Characteristics . Physical Classification....
Springer, 2023. — 224 p. — (CMS/CAIMS Books in Mathematics, 11). — ISBN 3031395239. This book provides a short introduction to partial differential equations (PDEs) . It is primarily addressed to graduate students and researchers , who are new to PDEs. The book offers a user-friendly approach to the analysis of PDEs, by combining elementary techniques and fundamental modern...
Harlow: Longman Higher Education, 1992. - 332p. This book addresses the theory and applications of mathematical models that involve (a) nonlinear operations; (b) differentiation; and (c) the presence of singular objects (like measures or non-differentiable functions). Classical nonlinear analysis can certainly deal with (a) and (b) , while the theory of distributions has proved...
Elsevier, Academic Press, 1994. — 446 p. Dedication Foreword General Existence of Solutions Theory Introduction Approximation of Solutions of Continuous Nonlinear PDEs Spaces of Generalized Functions Extending T(x, D) to the Order Completion of Spaces of Smooth Functions Existence of Generalized Solutions A Few First Examples Generalized Solutions as Measurable Functions...
(Oxford Texts in Applied and Engineering Mathematics) Publisher: Oxford University Press, USA, 2003. - 464 Pages. Partial differential equations are used in mathematical models of a huge range of real-world phenomena, from electromagnetism to financial markets. This new edition of Applied PDEs contains many new sections and exercises Including, American options, transform...
Springer, 2014. — 635 p. — (Undergraduate Texts in Mathematics). — ISBN10: 9400778198, ISBN13: 978-9400778191. This textbook is designed for a one year course covering the fundamentals of partial differential equations, geared towards advanced undergraduates and beginning graduate students in mathematics, science, engineering, and elsewhere. The exposition carefully balances...
Singapore: Springer, 2022. — 99 p. This volume is devoted to the study of hyperbolic free boundary problems possessing variational structure. Such problems can be used to model, among others, oscillatory motion of a droplet on a surface or bouncing of an elastic body against a rigid obstacle. In the case of the droplet, for example, the membrane surrounding the fluid in general...
Wiley, 2014. — 452 p. — 3rd ed. — ISBN: 1118629949, 9781118629949 A broad introduction to PDEs with an emphasis on specialized topics and applications occurring in a variety of fields Featuring a thoroughly revised presentation of topics, Beginning Partial Differential Equations, Third Edition provides a challenging, yet accessible,combination of techniques, applications, and...
2nd edition. — John Wiley & Sons, 2008. — 496 p. — ISBN: 0470133902. A rigorous, yet accessible, introduction to partial differential equations — updated in a valuable new edition. Beginning Partial Differential Equations, Second Edition provides a comprehensive introduction to partial differential equations (PDEs) with a special focus on the significance of characteristics,...
Wiley, 2014. — 130 p. — 3rd ed. — (Pure and Applied Mathematics). — ISBN: 1118630092, 9781118630099 As the Solutions Manual, this book is meant to accompany the main title, Beginning of Partial Differential Equations, Third Edition. The Third Edition features a challenging, yet accessible, introduction to partial differential equations, and provides a solid introduction to...
Springer, 2015. — 412 p. — ISBN: 3319201395, 9783319201399
This monograph provides the theoretical foundations needed for the construction of fundamental solutions and fundamental matrices of (systems of) linear partial differential equations. Many illustrative examples also show techniques for finding such solutions in terms of integrals. Particular attention is given to...
Springer, 2012. — 223 p. — ISBN: 3642244149 Partial differential equations of mixed elliptic-hyperbolic type arise in diverse areas of physics and geometry, including fluid and plasma dynamics, optics, cosmology, traffic engineering, projective geometry, geometric variational theory, and the theory of isometric embeddings. And yet even the linear theory of these equations is at...
Berlin: Logos Verlag Berlin, 2015. — 336 p. This thesis is concerned with the numerical solution of boundary value problems (BVPs) governed by nonlinear elliptic partial differential equations (PDEs). To iteratively solve such BVPs, it is of primal importance to develop efficient schemes that guarantee convergence of the numerically approximated PDE solutions towards the exact...
1997. - 415p. The book Partial Differential Equations through Examples and Exercises has evolved from the lectures and exercises that the authors have given for more than fifteen years, mostly for mathematics, computer science, physics and chemistry students. By our best knowledge, the book is a first attempt to present the rather complex subject of partial differential...
American Mathematical Society, 1982. — 169 p. — (Proceedings of Symposia in Pure Mathematics, vol. 4).
A collection of essays addressed at the meeting of proceedings of the fourth symposium in pure mathematics of the American Mathematical Society held at the University of California, Berkeley, California, April 21-22, 1960.
Extensions and Applications of the De Giorgi-Nash...
Springer International Publishing AG, 2017. — 469 p. — (Association for Women in Mathematics Series 5) — ISBN: 3319515918. This book is the second of a two volume series. Covering a range of subjects from operator theory and classical harmonic analysis to Banach space theory, this book features fully-refereed, high-quality papers exploring new results and trends in weighted...
Springer International Publishing, Switzerland, 2016. — 380 p. — (Association for Women in Mathematics Series. Volume 4). — ISBN: 9783319309590. Covering a range of subjects from operator theory and classical harmonic analysis to Banach space theory, this book contains survey and expository articles by leading experts in their corresponding fields, and features fully-refereed,...
La Habana: Ciencia y Tecnica, 1969. — 592 p. Lecciones sobre Ecuaciones en Derivadas Parciales del Profesor I. G. Petrovski es una amplia exposición del tema. En el Libro se estudia minuciosamente los diferentes tipos de Ecuaciones a Derivadas Parciales: Hiperbólicas, Elípticas y Parabólicas, así como el problemas de Cauchy y el Teorema de Kovalevskaya. Es un buen complemento a...
Amsterdam: De Gruyter, 2011. - 489p. This book presents a systematic approach to a solution theory for linear partial differential equations developed in a Hilbert space setting based on a Sobolev Lattice structure, a simple extension of the well established notion of a chain (or scale) of Hilbert spaces. The focus on a Hilbert space setting is a highly adaptable and suitable...
Cambridge: Cambridge University Press, 2022. — 203 p. Presenting the basics of elliptic PDEs in connection with regularity theory, the book bridges fundamental breakthroughs – such as the Krylov–Safonov and Evans–Krylov results, Caffarelli's regularity theory, and the counterexamples due to Nadirashvili and Vlăduţ – and modern developments, including improved regularity for...
Cambridge University Press, 2005. — 384 p.
A complete introduction to partial differential equations, this textbook provides a rigorous yet accessible guide to students in mathematics, physics and engineering. The presentation is lively and up to date, paying particular emphasis to developing an appreciation of underlying mathematical theory. Beginning with basic definitions,...
3rd Edition. — American Mathematical Society, 2011. — 534 p. — (Pure and Applied Undergraduate Texts, 15). — ISBN 0821868896, 9780821868898. Building on the basic techniques of separation of variables and Fourier series, the book presents the solution of boundary-value problems for basic partial differential equations: the heat equation, wave equation, and Laplace equation,...
Springer Netherlands 1979. — (Mathematical Physics Studies 1). — 140 pp. — ISBN: 978-90-277-1036-9 (Print) 978-94-009-9511-6 (Online).
The aim of this paper is to show that the theory of jet bundles supplies the appropriate setting for the study of Backlund trans formations. These transformations are used to solve certain partial differential equations, particularly non-linear...
Cambridge University Press, 2010. - 630 pages.
Do you want a rigorous book that remembers where PDEs come from and what they look like? This highly visual introduction to linear PDEs and initial/boundary value problems connects the math to physical reality, all the time providing a rigorous mathematical foundation for all solution methods. Readers are gradually introduced to...
Second Edition. — New York: Chapman and Hall/CRC, 2016. — 1623 p. Includes nearly 4,000 linear partial differential equations (PDEs) with solutions Presents solutions of numerous problems relevant to heat and mass transfer, wave theory, hydrodynamics, aerodynamics, elasticity, acoustics, electrodynamics, diffraction theory, quantum mechanics, chemical engineering sciences,...
Second Edition. — CRC Press, 2012. — 1912 pages. New to the Second Edition More than 1,000 pages with over 1,500 new first-, second-, third-, fourth-, and higher-order nonlinear equations with solutions Parabolic, hyperbolic, elliptic, and other systems of equations with solutions Some exact methods and transformations Symbolic and numerical methods for solving nonlinear PDEs...
CRC Press, 2022. — 402 p. — ISBN 978-1-032-11524-5. Separation of Variables and Exact Solutions to Nonlinear PDEs is devoted to describing and applying methods of generalized and functional separation of variables used to find exact solutions of nonlinear partial differential equations (PDEs). It also presents the direct method of symmetry reductions and its more general...
Academic Press, 2005. - 520 Pages.
Boundary Value Problems is the leading text on boundary value problems and Fourier series. The author, David Powers, has written a thorough, theoretical overview of solving boundary value problems involving partial differential equations by the methods of separation of variables. Professors and students agree that the author is a master at...
Boca Raton: CRC Press, 2016. - 292p.
The ordinary Laplacian is defined as the ordinary second derivative of a function of one variable or the sum of the ordinary second partial derivatives of a function of a higher number of variables in a physical or abstract Caresian space. Physically, the ordinary Laplacian describes an ordinary diffusion process in an isotropic medium...
World Scientific, 2004. — 193 p. — ISBN: 9812387641 This book presents, for the first time, a systematic formulation of the geometric theory of noncommutative PDE's which is suitable enough to be used for a mathematical description of quantum dynamics and quantum field theory. A geometric theory of supersymmetric quantum PDE's is also considered, in order to describe quantum...
Boston: de Gruyter, 2013. — 295 p. The text is intended for students who wish a concise and rapid introduction to some main topics in PDEs, necessary for understanding current research, especially in nonlinear PDEs. Organized on three parts, the book guides the reader from fundamental classical results, to some aspects of the modern theory and furthermore, to some techniques of...
Cambridge University Press, 2011. — 744 p. The partial differential equations that govern scalar and vector fields are the very language used to model a variety of phenomena in solid mechanics, fluid flow, acoustics, heat transfer, electromagnetism and many others. A knowledge of the main equations and of the methods for analyzing them is therefore essential to every working...
Birkhauser, 2008. — 472 p. The monograph is focused on presentation of recent results on some nonlinear parabolic-hyperbolic systems of partial differential equations arising from physics, mechanics and material science. Most of the results presented in this book are based on the original research of the author starting in 1997. The book is self-contained and the material is well...
Springer, 2012. — 181 p. — (Frontiers in Mathematics). — ISBN: 303480279X. This book presents recent results on nonlinear parabolic-hyperbolic coupled systems such as the compressible Navier-Stokes equations, and liquid crystal system. It summarizes recently published research by the authors and their collaborators, but also includes new and unpublished material. All models...
Springer, 2015. — 296 p. — (UNITEXT 92) — ISBN: 9783319154305, 9783319154312 This book provides a basic introduction to reduced basis (RB) methods for problems involving the repeated solution of partial differential equations (PDEs) arising from engineering and applied sciences, such as PDEs depending on several parameters and PDE-constrained optimization. The book presents a...
Atlantis Press, 2015. — 194 p. — (Atlantis Studies in Differential Equations 06). — ISBN 978-94-6239-126-0. By writing this book we wanted to present a new approach to impulsive boundary value problems, which is applicable both to the state-dependent and the fixed-time impulses. Existence results for boundary value problems with state-dependent impulses are rather rare in the...
Cairo, Egypt: Hindawi Publishing Corporation, 2008. — 205 p. — (Contemporary Mathematics and Its Applications 06). — ISBN: 9774540395. The book provides a comprehensive introduction to the mathematical theory of nonlinear problems described by elliptic partial differential equations. These equations can be seen as nonlinear versions of the classical Laplace equation, and they...
CRC Press, 2015. — 320 p. — ISBN: 9781498703413, EIBSN: 9781498703444 Partial Differential Equations with Variable Exponents: Variational Methods and Qualitative Analysis provides researchers and graduate students with a thorough introduction to the theory of nonlinear partial differential equations (PDEs) with a variable exponent, particularly those of elliptic type. The book...
3rd ed. — New Delhi: PHI Learning, 2011. — 499 p. — ISBN: 978-8120342224. The objective of this third edition is the same as in previous two editions: to provide a broad coverage of various mathematical techniques that are widely used for solving and to get analytical solutions to Partial Differential Equations of first and second order, which occur in science and engineering....
New York: Springer, 2022. — 558 p. The book serves as a primary textbook of partial differential equations (PDEs), with due attention to their importance to various physical and engineering phenomena. The book focuses on maintaining a balance between the mathematical expressions used and the significance they hold in the context of some physical problem. The book has wider...
Springer, 2004. — 447 p. Partial differential equations (PDEs) are fundamental to the modeling of natural phenomena, arising in every field of science. Consequently, the desire to understand the solutions of these equations has always had a prominent place in the efforts of mathematicians; it has inspired such diverse fields as complex function theory, functional analysis, and...
Walter de Gruyter, 2008. - 316 pages. ISBN10: 3110191539 This book deals with the reliable verification of the accuracy of approximate solutions which is one of the central problems in modern applied analysis. After giving an overview of the methods developed for models based on partial differential equations, the author derives computable a posteriori error estimates by using...
New York: Dover Publications, 1985. — 555 p. This first volume of a highly regarded two-volume text is fully usable on its own. After going over some of the preliminaries, the authors discuss mathematical models that yield first-order partial differential equations; motivations, classifications, and some methods of solution; linear and semilinear equations; chromatographic...
Mineola: Dover Publications, 2001. — 556 p. Second volume of a highly regarded two-volume set, fully usable on its own, examines physical systems that can usefully be modeled by equations of the first order. Examples are drawn from a wide range of scientific and engineering disciplines. The book begins with a consideration of pairs of quasilinear hyperbolic equations of the...
Birkhäusеr Bаsel, 2005, 282 pages Vsevolod Alekseevich Solonnikov is known as one of the outstanding mathematicians from the St. Petersburg Mathematical School. His remarkable results on exact estimates of solutions to boundary and initial-boundary value problems for linear elliptic, parabolic, Stokes and Navier-Stokes systems, his methods and contributions to the...
Springer-Verlag, 1978. — 154 p. — (Lecture Notes in Mathematics)
ISBN: 3540089519
The nonlinear method in the theory of distributions presented in this work is based on embeddings of the distributions in D' 0{ n) into associative and commutative algebras whose elements are classes of sequences of smooth functions on R n. The embeddings define various distribution...
Springer Basel, 2013. — 457 pages. ISBN10: 3034805128 This book primarily concerns quasilinear and semilinear elliptic and parabolic partial differential equations, inequalities, and systems. The exposition leads the reader through the general theory based on abstract (pseudo-) monotone or accretive operators as fast as possible towards the analysis of concrete differential...
Springer, 2024. — 180 p. Preface A Short Introduction to Reduced Basis Method Worked Out Problems for Beginners: Steady Cases Worked Out Problem 1: Steady Heat Conduction in a Thermal Block Worked Out Problem 2: A Linear Elasticity Problem on a Square Worked Out Problem 3: Thermal Transfer Problem in a Parametrized Geometry Worked Out Problem 4: A Transport Problem for the 2D...
Cham: Birkhäuser, 2023. — 241 p. This book collects papers related to the session “Harmonic Analysis and Partial Differential Equations” held at the 13th International ISAAC Congress in Ghent and provides an overview on recent trends and advances in the interplay between harmonic analysis and partial differential equations. The book can serve as useful source of information for...
2nd Edition. — Springer International Publishing, Switzerland, 2015. — 710 p. — ISBN: 978-3-319-15092-5. This book is designed as an advanced undergraduate or a first-year graduate course for students from various disciplines like applied mathematics, physics, engineering. It has evolved while teaching courses on partial differential equations (PDEs) during the last few years...
Springer, 2008. - 450 pages.
This book is designed as an advanced undergraduate or a first-year graduatecourse for students from various disciplines like applied mathematics,physics, engineering.
The main purpose is on the one hand to train the students to appreciate the interplay between theory and modelling in problems arising in the applied sciences; on the other hand to...
3rd Edition. — Springer International Publishing, Switzerland, 2016. — 699 p. — (UNITEXT – La Matematica per il 3+2. 99) — ISBN: 9783319312378 This book is designed as an advanced undergraduate or a first-year graduate course for students from various disciplines like applied mathematics, physics, engineering. It has evolved while teaching courses on partial differential...
Springer-Verlag Italia, 2013. — 480 pages. ISBN: 8847028612
This book is designed as an advanced undergraduate or a first-year graduate course for students from various disciplines like applied mathematics, physics, engineering. It has evolved while teaching courses on partial differential equations during the last decade at the Politecnico of Milan. The main purpose of these...
4th ed. — Springer, 2023. — 691 p. — (UNITEXT, 147). — ISBN 3031218523. This work is an updated version of a book evolved from courses offered on partial differential equations (PDEs) over the last several years at the Politecnico di Milano. These courses had a twofold purpose: on the one hand, to teach students to appreciate the interplay between theory and modeling in...
Springer, 2015. — 433 p. — ISBN: 978-3-319-15415-2. This book is designed for advanced undergraduate students from various disciplines, including applied mathematics, physics, and engineering. It evolved during the PDE courses that both authors have taught during recent decades at the Politecnico di Milano, and consists of problems of various types and difficulties. In the...
World Scientific Publishing, 2023. — 239 p. — (UTokyo Engineering Course/ Basic Mathematics). — ISBN 978-981-127-088-8. Quite a number of phenomena in science and technology, industrial and/or agricultural production and transport, medical and/or biological flows and movements, social and/or economical developments, etc., depend on many variables, and are very much complicated....
Cambridge University Press, 2001. - 385 pages.
This book provides an introduction to the use of geometric partial differential equations in image processing and computer vision. It brings a number of new concepts into the field, providing a very fundamental and formal approach to image processing. State-of-the-art practical results in a large number of real problems are...
London: London School of Economics, 2017. — 142 p. First Order PDEs. The classical trinity. Separation of variables. Integral transform methods. Distributions and weak solutions.
Springer, 2012. - 462 pages. This two-volume textbook provides comprehensive coverage of partial differential equations, spanning elliptic, parabolic, and hyperbolic types in two and several variables. In this first volume, special emphasis is placed on geometric and complex variable methods involving integral representations. The following topics are treated: integration and...
Springer, 2006. — 456 p. — ISBN10: 3-540-34457-8. This two-volume textbook provides comprehensive coverage of partial differential equations, spanning elliptic, parabolic, and hyperbolic types in two and several variables.In this first volume, special emphasis is placed on geometric and complex variable methods involving integral representations. The following topics are...
Springer, 2006. — 400 p. — ISBN10: 3-540-34461-6. This two-volume textbook provides comprehensive coverage of partial differential equations, spanning elliptic, parabolic, and hyperbolic types in two and several variables. In this second volume, special emphasis is placed on functional analytic methods and applications to differential geometry. The following topics are treated:...
Springer, 2012. - 469 pages.
This two-volume textbook provides comprehensive coverage of partial differential equations, spanning elliptic, parabolic, and hyperbolic types in two and several variables. In this second volume, special emphasis is placed on functional analytic methods and applications to differential geometry. The following topics are treated: solvability of...
Boca Raton: CRC Press, 2019. — 514 p. — ISBN: 1138580880. Variational Techniques for Elliptic Partial Differential Equations, intended for graduate students studying applied math. analysis, and/or numerical analysis, provides the necessary tools to understand the structure and solvability of elliptic partial differential equations. Beginning with the necessary definitions and...
Birkhauser, 2020. — 347 p. This monograph collects cutting-edge results and techniques for solving nonlinear partial differential equations using critical points. Including many of the author’s own contributions, a range of proofs are conveniently collected here, Because the material is approached with rigor, this book will serve as an invaluable resource for exploring recent...
World Scientific Publishing, 2021. — 407 p. — ISBN B089GQM3QD. 'This booklet provides a very lucid and versatile introduction to the methods of linear partial differential equations. It covers a wealth of very important material in a concise, nevertheless very instructive manner, and as such it may serve as an excellent guide to further, more advanced and detailed reading in...
World Scientific Publishing, 2017. — 262 p. — ISBN: 9789813226692. This book is directed toward the numerical integration (solution) of a system of partial differential equations (PDEs) that describes a combination of chemical reaction and diffusion, that is, reaction-diffusion PDEs. The particular form of the PDEs corresponds to a system discussed by Alan Turing and is...
Springer, 2021. — 339 p. This book investigates the close relation between quite sophisticated function spaces, the regularity of solutions of partial differential equations (PDEs) in these spaces and the link with the numerical solution of such PDEs. It consists of three parts. Part I, the introduction, provides a quick guide to function spaces and the general concepts needed....
American Mathematical Society, Providence, 2017. — 593 p. — ISBN 9781470436131. This is an introductory textbook about nonlinear dynamics of PDEs, with a focus on problems over unbounded domains and modulation equations. The presentation is example-oriented, and new mathematical tools are developed step by step, giving insight into some important classes of nonlinear PDEs and...
Basel: Birkhäuser, 2024. — 262 p. This volume presents recent advances and open problems in the cross section of infinite-dimensional systems theory and the modern treatment of PDEs. Chapters are based on talks and problem sessions from the first “Workshop on Systems Theory and PDEs” (WOSTAP), held at TU Bergakademie Freiberg in July 2022. The main topics covered include:...
Basel: Birkhäuser, 2022. — 321 p. This open access book provides a solution theory for time-dependent partial differential equations, which classically have not been accessible by a unified method. Instead of using sophisticated techniques and methods, the approach is elementary in the sense that only Hilbert space methods and some basic theory of complex analysis are required....
Providence: American Mathematical Society, 2013. — 354 p. On May 11, 2012, Professor Patrizia Pucci turned 60. In celebration of Patrizia Pucci’s birthday, a conference was held at the University of Perugia during May 28 and June 1, 2012. The main purpose of this scientific meeting has been to bring together leading experts and researchers in nonlinear partial differential...
Wiley. 2018. — 213 p. — ISBN: 978-1-119-50796-3. Solve engineering and scientific partial differential equation applications using the PDE2D software developed by the author This book derives and solves a range of ordinary and partial differential equation (PDE) applications. This book describes an easy-to-use, general purpose, and time-tested PDE solver developed by the author...
Princeton University Press, 2015. — 288 p. — ISBN: 0691161291. This textbook provides beginning graduate students and advanced undergraduates with an accessible introduction to the rich subject of partial differential equations (PDEs). It presents a rigorous and clear explanation of the more elementary theoretical aspects of PDEs, while also drawing connections to deeper...
Berlin: Springer, 2011. — 487 p. Along with finite differences and finite elements, spectral methods are one of the three main methodologies for solving partial differential equations on computers. This book provides a detailed presentation of basic spectral algorithms, as well as a systematical presentation of basic convergence theory and error analysis for spectral methods....
Springer, 2018. — 295 p. — (Operator Theory: Advances and Applications 26). — ISBN: 3319912135. This monograph surveys the theory of quantitative homogenization for second-order linear elliptic systems in divergence form with rapidly oscillating periodic coefficients in a bounded domain. It begins with a review of the classical qualitative homogenization theory, and addresses...
Princeton University Press, 2010 - 344 p. This book introduces a comprehensive methodology for adaptive control design of parabolic partial differential equations with unknown functional parameters, including reaction-convection-diffusion systems ubiquitous in chemical, thermal, biomedical, aerospace, and energy systems. Andrey Smyshlyaev and Miroslav Krstic develop explicit...
Dover Publications, 2006. — 352 p. — ISBN: 0486452972, 9780486452975
Geared toward students of applied rather than pure mathematics, this volume introduces elements of partial differential equations. Its focus is primarily upon finding solutions to particular equations rather than general theory.
Topics include ordinary differential equations in more than two variables,...
Walter de Gruyter, 2003. - 162 pages.
Modeling, in particular with partial differential equations, plays an ever growing role in the applied sciences. Hence its mathematical understanding is an important issue for today's research.
This book provides an introduction to three different topics in partial differential equations arising from applications. The subject of the...
World Scientific Publishing Company, 2004. - 320 pages. Second Edition
This textbook is a self-contained introduction to Partial Differential Equations (PDEs). It is designed for Undergraduate and first year graduate students who are mathematics, physics, engineering or, in general, science majors. The goal is to give an introduction to the basic equations of mathematical...
2nd edition. — John Wiley & Sons, 2007. — 464 p. — ISBN: 0470054565
Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing...
Hoboken: Wiley, 2007. — 691 p.
Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a...
Cambridge University Press, 2008. — 233 p. This book deals with equations that have played a central role in the interplay between partial differential equations and probability theory. Most of this material has been treated elsewhere, but it is rarely presented in a manner that makes it readily accessible to people whose background is probability theory. Many results are given...
Springer, 2007, 302p., 4th edition. The Direct Methods in the Calculus of Variations Lower Semi-continuity Constraints Compensated Compactness The Concentration-Compactness Principle Ekeland’s Variational Principle Duality Minimization Problems Depending on Parameters Minimax Methods The Finite Dimensional Case The Palais-Smale Condition A General Deformation Lemma The Minimax...
WSPC, 2024. — 414 p. Mathematical models are used to describe the essence of the real world, and their analysis induces new predictions filled with unexpected phenomena. In spite of a huge number of insights derived from a variety of scientific fields in these five hundred years of the theory of differential equations, and its extensive developments in these one hundred years,...
Berlin: de Gruyter, 2020. — 490 p. This authoritative monograph presents in detail classical and modern methods for the study of semilinear elliptic equations, that is, methods to study the qualitative properties of solutions using variational techniques, the maximum principle, blowup analysis, spectral theory, topological methods, etc. The book is self-contained and is...
Amsterdam: Springer, 1992. — 232 p. This volume provides a systematic introduction to the theory of the multidimensional Mellin transformation in a distributional setting. In contrast to the classical texts on the Mellin and Laplace transformations, this work concentrates on the local properties of the Mellin transforms, i.e. on those properties of the Mellin transforms of...
Oxford: Oxford University Press, 2015. — 514 p. This book, which is the first volume of two, presents a comprehensive treatment of aspects of classical and modern analysis relating to theory of ‘partial differential equations’ and the associated ‘function spaces’. It begins with a quick review of basic properties of harmonic functions and Poisson integrals and then moves into a...
Cambridge: Cambridge University Press, 2016. — 348 p. A careful and accessible exposition of a functional analytic approach to initial boundary value problems for semilinear parabolic differential equations, with a focus on the relationship between analytic semigroups and initial boundary value problems. This semigroup approach is distinguished by the extensive use of the ideas...
3rd ed. — Springer, 2023. — 733 p. — (Applied Mathematical Sciences, 115). — ISBN 3031338588. The first of three volumes on partial differential equations, this one introduces basic examples arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, in particular Fourier analysis, distribution theory,...
Springer, 2010. - 678 pages. The first of three volumes on partial differential equations, this one introduces basic examples arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, in particular Fourier analysis, distribution theory, and Sobolev spaces. These tools are then applied to the treatment...
Springer, 2010. — 614 Pages.
This second in the series of three volumes builds upon the basic theory of linear PDE given in volume 1, and pursues more advanced topics. Analytical tools introduced here include pseudodifferential operators, the functional analysis of self-adjoint operators, and Wiener measure. The book also develops basic differential geometrical concepts,...
3rd ed. — Springer, 2023. — 705 p. — (Applied Mathematical Sciences, 116). — ISBN 3031336992. This second in the series of three volumes builds upon the basic theory of linear PDE given in volume 1, and pursues more advanced topics. Analytical tools introduced here include pseudodifferential operators, the functional analysis of self-adjoint operators, and Wiener measure. The...
3rd ed. — Springer, 2023. — 773 p. — (Applied Mathematical Sciences, 117). — ISBN 3031339274. The third of three volumes on partial differential equations, this is devoted to nonlinear PDE. It treats a number of equations of classical continuum mechanics, including relativistic versions, as well as various equations arising in differential geometry, such as in the study of...
Springer, 2010. — 715 p.
The third of three volumes on partial differential equations, this is devoted to nonlinear PDE. It treats a number of equations of classical continuum mechanics, including relativistic versions, as well as various equations arising in differential geometry, such as in the study of minimal surfaces, isometric imbedding, conformal deformation, harmonic...
Basel: Birkhäuser, 1991. — 218 p. For the past 25 years the theory of pseudodifferential operators has played an important role in many exciting and deep investigations into linear PDE. Over the past decade, this tool has also begun to yield interesting results in nonlinear PDE. This book is devoted to a summary and reconsideration of some used of pseudodifferential operator...
Springer, 2019. — 176 p. — ISBN: 978-3-030-22590-2. The book presents a research area in geometric function theory concerned with harmonic quasiconformal mappings and hyperbolic type metrics defined on planar and multidimensional domains. The classes of quasiconformal and quasiregular mappings are well established areas of study in this field as these classes are natural and...
Berlin: de Gruyter, 2020. — 277 p. This is a clear, rigorous and self-contained introduction to PDEs for a semester-based course on the topic. For the sake of smooth exposition, the book keeps the amount of applications to a minimum, focusing instead on the theoretical essentials and problem solving. The result is an agile compendium of theorems and methods - the ideal...
World Scientific, 1994. - 350 pages. ISBN: 9810213514
This text is devoted to boundary value problems for general partial differential equations. It develops efficient methods of resolution of boundary value problems for elliptic equations, based on the theory of analytic functions, having great theoretical and practical importance. A new approach to the investigation of...
Cham: Springer Nature Switzerland, 2022. — 1221 p. This book provides a coherent, self-contained introduction to central topics of Analytic Partial Differential Equations in the natural geometric setting. The main themes are the analysis in phase-space of analytic PDEs and the Fourier–Bros–Iagolnitzer (FBI) transform of distributions and hyperfunctions, with application to...
Springer, 1998. - 392 Pages.
This book teaches the basic methods of partial differential equations and introduces related important ideas associated with the analysis of numerical methods for those partial differential equations. Standard topics such as separation of variables, Fourier analysis, maximum principles, and energy estimates are included. Numerical methods are...
Springer-Verlag, 2011. — 128 pages. — ISBN: 085729783X The subject of Partial Differential Equations (PDEs) which first emerged in the 18th century holds an exciting and special position in the applications relating to the mathematical modelling of physical phenomena. The subject of PDEs has been developed by major names in applied mathematics such as Euler, Legendre, Laplace...
Springer, 2018. — 175 p. — (Pseudo-Differential Operators: Theory and Applications 13). — ISBN: 331992706X. Classically developed as a tool for partial differential equations, the analysis of operators known as pseudodifferential analysis is here regarded as a possible help in questions of arithmetic. The operators which make up the main subject of the book can be characterized...
Cham: Springer, 2021. — 238 p. This textbook is devoted to second order linear partial differential equations. The focus is on variational formulations in Hilbert spaces. It contains elliptic equations, including some basic results on Fredholm alternative and spectral theory, some useful notes on functional analysis, a brief presentation of Sobolev spaces and their properties,...
2nd. ed. - Springer, 2023. - 266 p. - (UNITEXT, 154). - ISBN 3031359755. This textbook is devoted to second order linear partial differential equations. The focus is on variational formulations in Hilbert spaces . It contains elliptic equations , including the biharmonic problem, some useful notes on functional analysis, a brief presentation of Sobolev spaces and their...
3rd. ed. — Bookboon.com, 2018. — 172 p. The contents of this book came into existence during the time the author has been teaching a course on partial differential equations and on operator theory for about twenty years. Let us discuss the contents somewhat more closely. Basically, the book contains topics from distribution theory, from operator theory, and from operator...
3rd ed. — bookboon.com, 2018. — 248 p. Operators in Hilbert space. Operator semigroups and Markov processes. Holomorphic semigroups. Elements of functional analysis.
India: Krishna Parkashan Media (P) Ltd., 2021. — 219 p. — ISBN B095YBYMDH. Functions of several variables: Limit, continuity and differentiability of functions of several variables. Partial Derivatives: Partial derivatives and their geometrical interpretation, differentials, derivatives of composite and implicit functions, Jacobians, Chain rule, Euler’s theorem on homogeneous...
Kluwer Academic Publishers, 1989. — 454 p. — ISBN13: 978-94-010-7370-7. This special double issue of Acta Applicandae Mathematicae and two further issues to appear in the future, are devoted to recent developments in the theory of symmetries and conservation laws for general systems of partial differential equations. Symmetries and Conservation Laws of Partial Differential...
Springer Basel AG 2011. — 658 p. — (Monographs in Mathematics 101). — ISBN: 978-3-0346-0536-6. The theory of elliptic partial differential equations has undergone an important development over the last two centuries. Together with electrostatics, heat and mass diffusion, hydrodynamics and many other applications, it has become one of the most richly enhanced fields of...
Springer, Basel, 2014. — 796 p. — (Monographs in Mathematics. Volume 104) — ISBN: 3034808127 If we had to formulate in one sentence what this book is about, it might be "How partial differential equations can help to understand heat explosion, tumor growth or evolution of biological species". These and many other applications are described by reaction-diffusion equations. The...
Singapore: World Scientific, 2011. — 295 p. Fourier multiplier, function space X s p,q Navier-Stokes equation Strichartz estimates for linear dispersive equations Local and global wellposedness for nonlinear dispersive equations The low regularity theory for the nonlinear dispersive equations Frequency-uniform decomposition techniques Conservations, Morawetz' estimates of...
Springer, 2024. - 318 p. - ISBN 9819986915. This book focuses on the following three topics in the theory of boundary value problems of nonlinear second order elliptic partial differential equations and systems : (i) eigenvalue problem, (ii) upper and lower solutions method, (iii) topological degree method, and deals with the existence of solutions, more specifically...
CRC Press, 2021. — 299 p. — ISBN 978-0-367-71284-6. The parabolic partial differential equations model one of the most important processes in the real-world: diffusion. Whether it is the diffusion of energy in space-time, the diffusion of species in ecology, the diffusion of chemicals in biochemical processes, or the diffusion of information in social networks, diffusion...
N.-Y.: Springer, 2015. - 79p.
This book contains two review articles on the dynamics of partial differential equations that deal with closely related topics but can be read independently.
Wayne reviews recent results on the global dynamics of the two-dimensional Navier-Stokes equations. This system exhibits stable vortex solutions: the topic of Wayne's contribution is how...
Springer, 2009. — 700 p. — ISBN: 3642002501
"Partial Differential Equations and Solitary Waves Theory" is a self-contained book divided into two parts: Part I is a coherent survey bringing together newly developed methods for solving PDEs. While some traditional techniques are presented, this part does not require thorough understanding of abstract theories or compact concepts....
Department of Mathematics Saint Xavier University. — Beijing: Higher Education Press; Springer 2009. — 746 p. Nonlinear Physical Science focuses on recent advances of fundamental theories and principles,analytical and symbolic approaches, as well as computational techniques in nonlinear physical science and nonlinear mathematics with engineering applications.
Dover Publications, 1995. — 456 p. — ISBN: 0-486-68648-X. It has become customary at many colleges and universities to teach undergraduate courses in boundary value problems, Fourier series, and integral transforms. These courses usually emphasize the Fourier series or Laplace transforms, and then treat some problems in partial differential equations as applications. In...
New York: Chapman and Hall/CRC, 2013. — 182 p. Partial Differential Equations: Topics in Fourier Analysis explains how to use the Fourier transform and heuristic methods to obtain significant insight into the solutions of standard PDE models. It shows how this powerful approach is valuable in getting plausible answers that can then be justified by modern analysis.Using Fourier...
2nd. ed. — CRC Press, 2022. — 207 p. — ISBN 1032073160. Partial Differential Equations: Topics in Fourier Analysis, Second Edition explains how to use the Fourier transform and heuristic methods to obtain significant insight into the solutions of standard PDE models. It shows how this powerful approach is valuable in getting plausible answers that can then be justified by...
Springer, 1996. — 440 p. Abstract semilinear functional differential equations arise from many biological, chemical, and physical systems which are characterized by both spatial and temporal variables and exhibit various spatio-temporal patterns. The aim of this book is to provide an introduction of the qualitative theory and applications of these equations from the dynamical...
Springer, 2013. — 340 p. — ISBN: 3642368735, 3642368751 This book presents the various algebraic techniques for solving partial differential equations to yield exact solutions, techniques developed by the author in recent years and with emphasis on physical equations such as: the Maxwell equations, the Dirac equations, the KdV equation, the KP equation, the nonlinear...
New York: Springer, 2017. — 642 p. This book provides explicit representations of finite-dimensional simple Lie algebras, related partial differential equations, linear orthogonal algebraic codes, combinatorics and algebraic varieties, summarizing the author’s works and his joint works with his former students. Further, it presents various oscillator generalizations of the...
Laxmi Publications, 2021. — 201 p. Geometrical Meaning of a Differential Equation Exact Differential Equations Differential Equations of the First Order and Higher Degree Singular Solutions Orthogonal Trajectories Linear Differential Equations with Constant Coefficients Homogeneous Linear Ordinary Differential Equations Total Differential Equations Linear Differential Equations...
Springer, 2021. — 68 p. The classical Łojasiewicz gradient inequality (1963) was extended by Simon (1983) to the infinite-dimensional setting, now called the Łojasiewicz–Simon gradient inequality. This book presents a unified method to show asymptotic convergence of solutions to a stationary solution for abstract parabolic evolution equations of the gradient form by utilizing...
Springer, 2021. — 134 p. This second volume continues the study on asymptotic convergence of global solutions of parabolic equations to stationary solutions by utilizing the theory of abstract parabolic evolution equations and the Łojasiewicz–Simon gradient inequality. In the first volume of the same title, after setting the abstract frameworks of arguments, a general...
World Scientific Publishing Co. Pte. Ltd., 2006. — 202 p. — ISBN: 981-256-624-4 This is volume one of a two volume series. The intention is to provide a reference book for researchers in nonlinear partial differential equations and nonlinear functional analysis, especially for postgraduate students who want to be led to some of the current research topics. It could be used as a...
New York: McGrow Hill, 2011. - 250p. Classification and characteristics Qualitative behavior of solutions to elliptic equations Qualitative behavior of solutions to evolution equations First-order equations Eigenfunction expansions and integral transforms : theory Eigenfunction expansions and integral transforms : applications Green's functions Different methods for parabolic...
Springer, 2017. — 171 p. — (Lecture Notes in Mathematics). — ISBN10: 3319520954. — ISBN13: 978-3319520957. Studying the fine properties of solutions to Stochastic (Partial) Differential Equations with reflection at a boundary, this book begins with a discussion of classical one-dimensional diffusions as the reflecting Brownian motion, devoting a chapter to Bessel processes, and...
Singapore: World Scientific Publishing Company, 2025. - 632 p. - ISBN 9811298505. Partial Differential Equations (PDEs) are fundamental in fields such as physics and engineering, underpinning our understanding of sound, heat, diffusion, electrostatics, electrodynamics, thermodynamics, fluid dynamics, elasticity, general relativity, and quantum mechanics. They also arise in...
Springer International Publishing AG, 2016. — 186 p. — (Lecture Notes in Mathematics 2174) — ISBN: 3319467379 Focusing on p-adic and adelic analogues of pseudodifferential equations, this monograph presents a very general theory of parabolic-type equations and their Markov processes motivated by their connection with models of complex hierarchic systems. The Gelfand-Shilov...
Springer, 2020. — 96 p. — (SpringerBriefs in Applied Sciences and Technology: Continuum Mechanics). — ISBN: 978-3-030-35310-0. The derivation and understanding of Partial Differential Equations relies heavily on the fundamental knowledge of the first years of scientific education, i.e., higher mathematics, physics, materials science, applied mechanics, design, and programming...
London: World Scientific, 2022. — 283 p. — ISBN 9781800612686. The Qualitative Theory of Ordinary Differential Equations (ODEs) occupies a rather special position both in Applied and Theoretical Mathematics. On the one hand, it is a continuation of the standard course on ODEs. On the other hand, it is an introduction to Dynamical Systems, one of the main mathematical...
Текст лекцій. — Львів: Тріада плюс, 2004. — 178 с. Текст лекцій відповідає університетському курсу рівнянь у частинних похідних для математичних спеціальностей. У ньому викладені традиційні для цього курсу питання такі, як класифікація та зведення до канонічного вигляду рівнянь другого порядку, формулювання та дослідження коректності основних задач для рівнянь гіперболічного,...
М.: Наука, 1978. — 352 с. Монография, написанная крупным французским математиком Адамаром, представляет собой классический труд по теории линейных уравнений с частными производными. В книге впервые построено фундаментальное решение линейного гиперболического и эллиптического уравнения второго порядка с переменными коэффициентами. Обсуждается вопрос о принципе Гюйгенса. Содержание....
Учебное пособие. — Красноярск: Сибирский федеральный университет (СФУ), 2011. — 88 с. — ISBN 978-5-7638-2176-5. Рассмотрены основные уравнения математической физики, некоторые методы решения дифференциальных уравнений в частных производных второго порядка. Предназначено для студентов электромеханических, теплоэнергетических и радиотехнических специальностей. Вводные понятия и...
Ростов н/Д: ЮФУ, 2009. — 80 с. Данное учебное пособие является результатом значительной переработки четырех методических указаний Алексеева А. Д., Радченко Т. Н., Рогожина В. С. и Хасабова Э. Г., опубликованных в УПЛ РГУ в 1992 году. Добавлено много новых задач, приведены подробные решения стандартных задач. Расширена теоретическая часть. Пособие будет полезно при изучении...
М.: Наука. Гл. ред. физ.-мат. лит., 1991. — 353 с. — (СМБ). Излагается метод численного решения граничных задач, позволяющий получить приближенные решения почти всех классических внутренних и внешних граничных задач математической физики. Метод основан на разложении функции в ряды по фундаментальным решениям (функциям) соответствующих дифференциальных операторов. Исследуются...
2-е изд., доп. — М.: Фазис, 1997. — 175 с.: ил. — (Библиотека студента-математика ; вып.2).
Лекции великого современного математика, который поставил себе целью изложить ряд главных идей современной математической физики - теорию одного уравнения в частных производных, принцип Гюйгенса в теории волн, вариационный принцип в теории колебаний и т. д. Глубоко и интересно изложена так...
Электронное издание. — М.: МЦНМО, 2018. — 181 с. — ISBN: 978-5-4439-3174-6. Данный курс был разработан и прочитан выдающимся математиком В. И. Арнольдом в Независимом московском университете. Помимо традиционных вопросов курса уравнений с частными производными (метод Даламбера, метод Фурье, краевые задачи и т. д.) автор уделяет большое внимание взаимодействию с другими...
М.: Наука, Физматлит, 1965. — 340 c. Задача Дирихле для общего нелинейного эллиптического уравнения второго порядка. Квазилинейные эллиптические уравнения со слабыми нелинейностями. Квазилинейные эллиптические уравнения с сильными нелинейностями. Уравнения Монжа-Ампера (теория обобщенных решений). Реулярные решения уравнений Монжа-Ампера.
Красноярск: СФУ, 2007. — 140 с. В учебном пособии рассматриваются различные методы решения дифференциальных уравнений: метод слабой аппроксимации, метод Галеркина, метод Фурье. Излагается теория операторных уравнений, которая позволяет успешно исследовать разрешимость краевых задач для уравнений в частных производных. Вспомогательные сведения Неравенства Некоторые понятия...
Перевод с англ. — М.: Мир, 1964. — 303 с. В этой монографии изложены основы развитого автором метода интегральных представлений решений линейных уравнений с частными производными. В основе метода лежит получение классов решений этих уравнений из аналитических функций при помощи специальных интегральных операторов. В книге рассматриваются уравнения и системы с двумя и тремя...
Ред. и комент. Н.И. Ахиезера. — Харьков: Изд-во Харьковск. гос. ун-та им. А.М. Горького, 1956. — 95 с. Давно известны примеры дифференциальных уравнений с частными производными второго порядка, все решения которых являются аналитическими функциями своих аргументов. Классический пример представляет уравнение Лапласа. Одною из своих знаменитых «математических проблем», предложенных...
М.: Мир, 1966. — 352 с.
В основу книги положен курс лекций по теории уравнений с частными производными, прочитанный на семинаре по прикладной математике, который был организован Американским математическим обществом.
Книга освещает современное состояние теории; наряду с известными, ставшими уже классическими результатами и методами, в ней излагаются достижения последних лет,...
В сборнике: Труды математического института имени В. А. Стеклова. Т.41. М.: Издательство Академии наук СССР, 1953. — 59 с. Не распознано Оглавление (3 главы): Глава. Задача Т Постановка задачи Т Принцип экстремума Единственность решения Доказательство существования решения Продолжение Глава. Некоторые простейшие обобщения задачи Т Задача Т1 Принцип экстремума и доказательство...
М.: Наука, 1966. — 203 с. Настоящая монография является переработанным и дополненным вариантом лекционного курса по нефредгольмовым эллиптическим краевым задачам, прочитанного автором в Новосибирском государственном университете в 1964 — 1965 учебном году. Она посвящена изучению основных линейных краевых задач для линейных дифференциальных уравнений с частными производными второго...
М.: Издательство Академии наук СССР, 1959. — 164 с. Не распознано Содержание: Общие замечания о линейных дифференциальных уравнениях с частными производными смешанного типа Уравнение второго порядка с двумя независимыми переменными Теория Чибрарио Система двух уравнений с частными производными первого порядка Линейные системы уравнений с частными производными второго порядка с...
Учебное пособие. — Москва: МИСИ — МГСУ, 2023. — 67 с. Учебное пособие составлено в соответствии с программой дисциплины «Уравнения математической физики» и знакомит с основными методами, инструментами и сферами использования уравнений математической физики в различных областях науки. Представлены теоретические вопросы, примеры и практические задания по изучаемому курсу для...
Конспект лекций. — Минск: Белорусский государственный университет информатики и радиоэлектроники (БГУИР), 2009. — 120 с. — ISBN 978-985-488-429-5. Издание посвящено дифференциальным уравнениям в частных производных, подходам к их моделированию, аналитическим и некоторым численным методам их решения. Подробно разобраны примеры компьютерного моделирования в среде MatLAB.
Львів: ЛНУ ім. І. Франка. Посібник для студентів 3-го курсу механіко-математичного факультету. Містить допоміжні розділи до курсу "Рівняння у частинних похідних" (РЧП) такі, як: відомості з математичного і функціонального аналізу, моделювання фізичних процесів за допомогою РЧП, задачі на власні значення, теореми Фредгольма для інтегральних рівнянь.
М.-Л.: ОГИЗ, Государственное издание технико-технической литературы, 1948. — 296 с. На базе теории функций комплексной переменной развиваются специальные методы для изучения одного класса дифференциальных уравнений эллиптического типа, охватывающего много важных уравнений математической физики.
М.: Московский центр непрерывного математического образования (МЦНМО), 2021. — 365 с. Книга посвящена основам алгебраического и геометрического подхода к теории нелинейных дифференциальных уравнений. Она включает в себя идеи из теории интегрируемых систем, формальной теории дифференциальных уравнений в ее современной когомологической форме, данной Д. Спенсером и Х....
М.: Наука. Гл. ред. физ.-мат. лит., 1986. — 336 с. Изложение нового направления в теории нелинейных дифференциальных уравнений, возникшего на стыке коммутативной алгебры, дифференциальной геометрии и теории дифференциальных уравнений в частных производных. Для общих систем нелинейных дифференциальных уравнений с единой геометрической точки зрения трактуются такие вопросы, как...
Современная математика. Фундаментальные направления. Том 30 (2008). С. 3–173.
О разрешимости и оценках решений ФДУ параболического типа в пространствах Соболева.
О гладких решениях функционально-дифференциальных уравнений. Условия согласования.
Корректная разрешимость уравнений гиперболического типа с последействием в гильбертовом пространстве.
Описание характеристических...
Учебное пособие. — М.: МИИТ, 2010. — 134 с. В первой главе описано преобразование связывающее решения квазилинейных обыкновенных дифференциальных уравнений с решениями полулинейных уравнений. С помощью этого преобразования вычислены асимптотические представления решения квазилинейного ОДУ возникающего из важных в приложениях уравнений. Во второй главе проводится изложение...
Учебное пособие .— Красноярск: КГПУ им. П.П. Астафьева, 2007. — 118 с. — ISBN: 978-5-85981-269-1 Предназначено для студентов IV -V курсов математического факультета КГПУ и содержит теоретический материал и задачи для спецкурса по теории дифференциальных уравнений в частных производных. Введение Волновое уравнение Канонический вид линейного уравнения второго порядка с двумя...
Воронеж: Воронеж. гос. ун-т, 2005. - 75 с. Учебно-методическое пособие содержит теоретический материал, необходимый для усвоения спецкурсов, в которых рассматриваются дифференциальные уравнения с частными производными второго порядка эллиптического типа. Пособие подготовлено на кафедре математического анализа математического факультета Воронежского государственного университета.
Учебное пособие. — Москва: Московский государственный университет (МГУ) имени М.В. Ломоносова, 1999. — 96 с. В пособии изучаются уравнения с частными производными первого порядка. Рассмотрены вопросы локального существования гладких решений задачи Коши для линейных, квазилинейных и нелинейных уравнений. Подробно изложена теория разрывных обобщенных решений для квазилинейного...
Учебное пособие. — М.: МГУ, 1999. — 96 с.
В пособии изучаются уравнения с частными производными первого порядка. Рассмотрены вопросы локального существования гладких решений задачи Коши для линейных, квазилинейных и нелинейных уравнений. Пособие содержит большое количество оригинальных задач и упражнений, многие вопросы излагаются на примере их решения.
М.; Л.: Государственное объединенное научно-техническое издательство НКТП СССР: Редакция технико-теоретической литературы, 1938. — 274 с. Предлагаемая книга, могущая служить введением в различные ветви теории дифференциальных уравнений с частными производными, примыкает к двум томам собрания Шуберта (Sammlung Schubert), трактующим об обыкновенных дифференциальных уравнениях...
Ленинград, Москва: ОНТИ, 1934. — 360 с. Основанием этого курса служат лекции, читанные автором в Ленинградском университете в 1921/22 и 1928/29 годах, а также лекции, прочитанные там же небольшому кружку студентов весною 1931 года, на которых было изложено содержание последних трех глав почти в том виде, в каком они находятся в курсе. Предисловие Введение. Некоторые теоремы из...
Учебное пособие. — Новосибирск: Новосибирский государственный университет (НГУ), 2015. — 270 с. Излагаются некоторые сведения из теории соболевских пространств, необходимые при изучении курсов по дифференциальным уравнениям с частными производными и уравнениям математической физики. Подробно обсуждается понятие обобщенной производной. Доказываются теоремы вложения. Изучаются...
М.: Наука 1987. — 416 с. Посвящается исследованию краевых задач для эллиптических систем и начально-краевых (смешанных) задач для многомерных систем уравнений с частными производными. Исследование указанных задач проводится на основе единого метода — метода сингулярных интегральных уравнений по областям с краями. Излагается систематическая теория класса систем сингулярных...
М.: Наука, 1971. — 228 с. Монография посвящена постановке и исследованию граничных задач для системы дифференциальных уравнений с частными производными составного типа. Она содержит результаты исследования автора, полученные за последние годы. Основное внимание в монографии уделено вопросам нормальной разрешимости и получению явных формул для индекса граничных задач. Книга...
Ташкент: Фан, 1979. — 120 с. В монографии ставятся и исследуются корректные краевые задачи для различных типов уравнений с частными производными второго, третьего и четвертого порядков. Приложения рассматриваемых уравнений встречаются в различных задачах механики. Издание предназначено для специалистов по дифференциальным уравнениям и их приложениям, аспирантов и студентов...
Допоміжні розділи рівнянь в частинних похідних. Лекції для студентів 3 курсу механіко-математичного факультету.
Моделювання фізичних процесів за допомогою рівнянь в частинних похідних. Задачі на власні значення для звичайних диференціальних рівнянь та рівнянь в частинних похідних. Теореми Фредгольма для інтегральних рівнянь.
Конспект лекций. — Нальчик: Каб.-Балк. ун-т, 2003. — 109 с. Издание содержит задачи, обеспечивающие высокий уровень доступности материала, а также необходимый дополнительный теоретический материал с комментариями. Приводится большой обзор литературы к каждой главе. Предназначено для студентов всех форм обучения по специальности "математика". Введение 3 Задача Коши для...
Электронное учебно-методическое пособие. — Нижний Новгород: Нижегородский государственный университет им. Лобачевского Н.И., 2012. — 82 с.
В учебно-методическом пособии изучаются вопросы современной теории краевых задач для уравнений математической физики. Вводится понятие обобщённого решения задач для дифференциальных уравнений с частными производными. Обсуждаются свойства...
М.: Издание Московскаго математическаго общества, 1916. — 412 с. Различные виды интегралов уравнения с частными производными 1-го порядка. Вывод из полного интеграла особенных и общих решений способом изменения произвольных постоянных, основываясь на свойствах функциональных определителей. Частные виды общего интеграла, которые приводят к уравнениям, линейным в отношении...
Пер. Н.Д. Введенская, ред. С.Г. Михлин. — М.: Издательство иностранной литературы, 1958. — 156 с. В небольшой монографии Ф. Иона с достаточной полнотой обрисованы некоторые новые возможности классического метода плоских волн и сферических средних применительно к дифференциальным уравнениям с частными производными. Можно считать, что в этом направлении книга является дополнением...
Москва: МГТУ им. Н.Э. Баумана, 2018. — 105 с. Одномерное волновое уравнение. Метод Фурье. Преобразование Фурье. Обобщенные функции. Фундаментальное решение. Специальные функции.
М.: МГТУ им. Н.Э. Баумана, 2019. — 106 с. Введение. Одномерное волновое уравнение. Метод Фурье. Преобразование Фурье. Обобщенные функции. Фундаментальное решение. Специальные функции. Литература. А4 формат
Л.-М.: ОНТИ. Гл. ред. общетехн. лит., 1936. — 528 с. В научной монографии дается систематическое изложение методов приближенного решения граничных задач для дифференциальных уравнений в частных производных эллиптического типа. Наибольшее внимание уделено уравнениям Лапласа, Пуассона и бигармоническому уравнению, вопросы решения которых имеют весьма важное значение в...
М.: Физматлит, 2009. — 184 с. — ISBN: 978-5-9221-1155-3. В монографии представлен ряд методов построения точных решений линейных и нелинейных уравнений с частными производными. Изложение ведется в рамках двух основных парадигм: непрерывные преобразования и инвариантность. Особое внимание уделяется таким подходам, как методы интегрирования Дарбу, Эйлера, Беклунда, Мутара. Дано...
Учебно-методическое пособие. — Москва: Московский государственный университет (МГУ) имени М.В. Ломоносова, 1993. — 160 с. Пособие предназначено для студентов, начинающих изучать уравнения с частными производными и уравнения математической физики. Оно может быть использовано также для самообразования. Предисловие. Гиперболические уравнения. Метод характеристик. Метод Фурье....
Учебное пособие. — Томск: Томский политехнический университет (ТПУ), 2011. — 48 с. Излагаются основные понятия об уравнениях в частных производных. Охват материала соответствует программе университетского курса для студентов элитного технического образования Томского политехнического университета в рамках курса математики. Предназначено для студентов, аспирантов,...
Монография. — Минск: БГУ, 2013. — 368 с. — ISBN: 978-985-518-843-9. Излагается метод энергетических неравенств и операторов осреднения с переменным шагом при изучении корректной разрешимости граничных задач для дифференциальных уравнений с частными производными. Рассмотрены на примере разных задач сильные и слабые решения, где расширения операторов рассматриваемых...
СПб: Издание физико-математического факультета С.-Петербургского университета, 1911. — 469 с. Рассуждение об определении произвольных функций в интегралах уравнений с частными производными. Диссертация на степень магистра чистой и прикладной математики. О совокупных уравнениях с частными производными первого порядка и некоторых вопросах математики. Диссертация на степень...
Екатеринбург: ГОУ ВПО УГТУ-УПИ, 2004. – 214 с. - ISBN: 5-321-00430-7 Рассмотрены основные вопросы, относящиеся к теории уравнений с частными производными и методам математической физики. Описываются постановки основных краевых задач математической физики, указываются методы их аналитического и приближенного решения. Разбираются конкретные примеры и приводятся упражнения для...
Учебное пособие — М.: Мех-Мат. МГУ, 1969. — 105 с. Настоящий курс лекций по нелинейным уравнениям с частными производными состоит из двух частей: эллиптические и параболические уравнения второго порядка - часть I, уравнения первого порядка - часть II. Отдельно предполагается изложить дополнения к этому курсу лекций. То обстоятельство, что первая часть посвящена уравнениям...
М.: МИАН, 2010. — 122 с. — (Лекционные курсы НОЦ; вып. 16). Серия «Лекционные курсы НОЦ» — рецензируемое продолжающееся издание Математического института им. В. А. Стеклова РАН. В серии «Лекционные курсы НОЦ» публикуются материалы специальных курсов, прочитанных в Математическом институте им. В. А. Стеклова Российской академии наук в рамках программы Научно-образовательный центр...
Учебник для студентов технических учебных заведений. — Л.: Артиллерийская академия, 1933. — 334 с. Состоит из разделов: Линейные уравнения с частными производными первого порядка. Нелинейные уравнения с частными производными первого порядка. Уравнения с частными производными второго порядка одной неизвестной функции. Уравнения с частными производными первого и второго порядков...
Кемеровский государственный университет. — Кемерово, 2012. — 116 с. — ISBN: 978-5-8353-1338-9. Учебное пособие посвящается теории краевых задач для нелинейных эллиптических систем дифференциальных уравнений первого порядка с двумя независимыми переменными общего вида. Пособие предназначено для студентов и аспирантов высших учебных заведений, специализирующихся по...
М.: Наука, 1967. - 736 с.
В книге исследованы линейные уравнения с разрывными и гладкими коэффициентами, квазилинейные уравнения с дивергентной главной частью, квазилинейные уравнения общего вида, системы линейных и квазилинейных уравнений.
Для студентов старших курсов и аспирантов.
Изд. второе, переработанное. — М.: Наука, 1973. — 576 с. Книга посвящена линейным и квазилинейным эллиптическим уравнениям второго порядка. В ней проводятся качественные исследования решений этих уравнений и на их базе устанавливается разрешимость в целом классических краевых задач. Книга содержит изложение основных достижений, полученных в данной области и опубликованных лишь в...
М. : Наука, 1971. — 288 с. Книга посвящена теории эллиптических и параболических уравнений 2-го порядка, главным образом, линейных. Значительное внимание уделено качественным вопросам поведения решений вблизи граничных точек и на бесконечности.
М.: Мир, 1972. — 588 с. Автор книги — известный французский математик, труды которого уже знакомы читателю (Латтес Р., Лионс Ж.-Л., «Метод квазиобращения и его приложения», «Мир», 1970; Лионс Ж.-Л., Мадженес Э., «Неоднородные граничные задачи и их приложения», «Мир», 1971). Его новая монография посвящена некоторым методам решения нелинейных уравнений в частных производных. Эти...
Учебное пособие. Новосибирск, 2016, 112 с.
Конспект семинарских (практических) занятий по курсу "Уравнения математической физики", проводившихся автором на 3 курсе механико-математического факультета Новосибирского государственного университета в течение 2000-х годов. Для студентов математических специальностей и их преподавателей.
Учебник. – М.: Российский университет дружбы народов (РУДН), 1997. — 447 с Учебник написан на основе лекций, читаемых автором на факультете физико-математических и естественных наук Российского университета дружбы народов. В книге отражены следующие темы: выводы основных уравнений математической физики и гидродинамики; общая теория дифференциальных уравнений в частных...
Перевод с японского Ю.В. Егорова. — М.: Мир, 1977. — 504 с. Книга представляет собой написанный на высоком научном уровне учебник по уравнениям с частными производными. Она содержит изложение важнейших разделов современной теории дифференциальных уравнений. Книга рассчитана на студентов и аспирантов математических и физических факультетов университетов и педвузов.
Волгоград: ВГУ, 2009. — 140 с.
Приводится цикл статей, посвященных почти решениям нелинейных уравнений с частными производными. В большинстве приложений дифференциальных уравнений в естествознании на самом деле мы имеем дело не с (идеальными) решениями уравнений, но с функциями, "близкими"к истинным решениям. В процессе приближенного вычисления мы также находим лишь функцию,...
М.: Изд-во иностранной литературы, 1957. — 255 с.
Книга представляет собой единственный в современной литературе систематический обзор теории эллиптических уравнений с частными производными. Подробно изложены наиболее важные разделы теории линейных и нелинейных эллиптических уравнений второго порядка. Библиография содержит более шестисот названий работ, опубликованных главным...
М.: Наука, 1976. — 391 с. В книге рассматриваются основные краевые задачи для эллиптических и задача Коши и смешанные задачи для гиперболических и параболических уравнений второго порядка. Широко используется понятие обобщенного решения. Для чтения книги достаточно владеть основами математики в размере программы первых двух курсов механико-математических или физических факультетов...
Душанбе: Дониш, 1986. — 116 с. Монография посвящена некоторым классам систем уравнений в частных производных со многими независимыми переменными. К ним относятся, в частности, комплексные системы обобщенных уравнений Коши-Римана и системы уравнений Бельтрами. Основное внимание уделяется методам исследования совместности переопределенных систем и построению многообразия решений.
Учебное пособие. — Курган: Курганский государственный университет, 2022. — 76 с. — ISBN 978-5-4217-0623-6. Учебное пособие состоит из двух глав. Целью учебного пособия является знакомство студентов с методами решения уравнений с частными производными. В первой главе дается обзор методов решения уравнений с частными производными первого порядка. Во второй главе рассматриваются...
М.: Высшая школа, 1977. — 431 с.: ил. В книге исследуются три классических типа уравнений математической физики: эллиптический, параболический и гиперболический. Изложение проводится для пространства любого числа измерений с широким привлечением методов функционального анализа и понятия обобщенных решений. Предназначается для студентов-математиков, а также для аспирантов и...
Перевод с японского. — М.: Мир, 1967. — 132 с. Книга, написанная видным японским специалистом, входит в серию „Современная математика", выпускаемую японским издательством „Кёрицу". В ней очень сжато рассмотрены важнейшие вопросы современной теории уравнений и систем уравнений эллиптического и гиперболического типа. В основе изложения лежит функционально-аналитический подход,...
Сочинение, удостоенное премии Заслуженного Профессора Брашмана. — М.: Издание Императорскаго Московскаго Университета, 1880. — 210 с. Краткий исторический очерк. О выводе метода Ли для интегрирования нелинейных совместных уравнений из метода Майера и о применении метода Ли в интеграции одного уравнения. О нахождении полного интеграла уравнения второго порядка с двумя независимыми...
М.: Издательство иностранной литературы, 1962. — 279 с. В этой книге известный метод Винера-Хопфа, разработанный для решения определенного класса интегральных уравнений, применяется к решению краевых задач для дифференциальных уравнений в частных производных. Рассматриваются примеры из теории электромагнитных волн, акустики, гидродинамики, теории упругости и теории потенциала....
6-е изд. — М.: Лаборатория знаний, 2020. — 263 c. — (Классический университетский учебник). — ISBN: 978-5-00101-703-5. В книге излагаются основные факты, относящиеся к уравнению Лапласа, уравнению теплопроводности и волновому уравнению как простейшим представителям трех основных классов уравнений с частными производными. Приводятся доказательство теоремы Ковалевской, смешанная...
Соросовский образовательный журнал ‹ N, 1997. С. 116-121 Теорема Ковалевской о существовании аналитических (то есть представимых в виде степенных рядов) решений уравнений с частными производными находит многочисленные применения во всех важнейших разделах современной теории дифференциальных уравнений и смежных областях математики. Ее использование существенно в доказательствах...
М.: Наука, 1987. — 424 с. Во вторую книгу избранных трудов академика И.Г. Петровского включены его работы по уравнениям с частными производными, относящиеся главным образом к теории уравнений с частными производными второго порядка, обзорные статьи, работы по исследованию особых точек и предельных циклов систем обыкновенных дифференциальных уравнений, работы но теории...
М.: Наука, 1986. — 508 с. Настоящее издание представляет собой первую книгу избранных трудов академика И.Г. Петровского. Она содержит основные работы И. Г. Петровского по системам уравнений с частными производными и алгебраической геометрии. Публикуемые работы И.Г. Петровского по системам уравнений с частными производными заложили основы современной теории систем уравнений с...
Москва; Ленинград: Государственное издательство технико-теоретической литературы (ГИТТЛ), 1950. — 303 с. Предисловие. Введение. Классификация уравнений. Определения. Примеры. Задача Коши. Теорема Ковалевской. Обобщение задачи Коши. Понятие о характеристике. О единственности решения задачи Коши в области неаналитических функций. Приведение к каноническому виду в точке и...
Москва; Ленинград: Государственное издательство технико-теоретической литературы (ГИТТЛ), 1961. — 400 с. Предисловие Введение. Классификация уравнений Определения. Примеры Задача Коши. Теорема Ковалевской Обобщение задачи Коши. Понятие о характеристике О единственности решения задачи Коши в области неаналитических функций Приведение к каноническому виду в точке и классификация...
Екатеринбург: Уральский федеральный университет имени первого президента России Б.Н. Ельцина (УрФУ), 2014. — 134 с. В книге приводятся численные алгоритмы решения дифференциальных уравнений в частных производных с эффектом запаздывания. Для обоснования сходимости дается общая разностная схема решения функционально-дифференциальных уравнений, к которой затем сводятся различные...
Монография. — М.: Мир, 1983. — 400 с. Монография известного французского математика, посвященная «формальной» теории уравнений с частными производными, интерес к которой в последнее время сильно вырос. Основным инструментом теории является новый и весьма содержательный алгебраический формализм, разработанный Э Картаном, С. Ли, Д. Спенсером и др. Русское издание дополнено новым...
Учебно-практическое пособие. — М.: Альфа-Пресс, 2009. — 90 с. — ISBN: 978-5-94280-428-2. СПбГУ, факультет "Прикладная математика и процессы управления". В учебно-практическом пособии рассмотрены основные методы и приемы решения уравнения в частных производных. Приведенные в учебном материале примеры и задачи позволяют успешно овладеть знаниями по изучаемой дисциплине. Пособие...
Учебное пособие. — Самара: Самарский государственный университет (СГУ), 2004. — 140 с. Пособие предназначено для студентов механико-математического факультета, изучающих курс «Дифференциальные уравнения в частных производных». Также может быть полезно для аспирантов соответствующих специальностей и студентов других факультетов и вузов, изучающих уравнения математической физики.
Самара: Изд-во Самарского университета, 2020. — 72 с. Учебное пособие предназначено для обучающихся университета, по основной образовательной программе высшего образования по направлению подготовки 01.05.01 Фундаментальная математика и механика, изучающих курс «Уравнения в частных производных». Цель его – познакомить обучающихся с современными методами исследования разрешимости...
Учебное пособие. — Ростов-на-Дону; Таганрог: Южный федеральный университет (ЮФУ), 2022. — 132 с. Пособие посвящено основам работы в пакете FlexPDE, который предназначен для построения численных решений дифференциальных уравнений в частных производных с помощью метода конечных элементов. Описаны основные разделы типовой программы. Для демонстрации и эффективного освоения...
Ташкент: Фан, 1988. — 186 с. — ISBN 5-648-00026-Х. В монографии рассмотрена общая нестационарная задача с неизвестной границей и получены условия ее разрешимости. Как частный случай исследованы многомерные задачи Стефана, Веригина, задача кристаллизации бинарных сплавов и т.д. Локальность задачи позволяет сводить вопрос о существовании решения исходной задачи к вопросу о...
Учебное пособие. — СПб.: Санкт-Петербургский государственный университет (СПбГУ), 2019. — 204 с. Учебное пособие основано на курсах лекций, прочитанных автором студентам бакалавриата и магистратуры математико-механического факультета СПбГУ. В нем излагаются некоторые разделы прикладной теории дифференциальных уравнений в частных производных. В частности, рассматривается...
М.; Л.: Гостехиздат, 1947. — 354 с. Книга включает сведения об алгебре косых форм и о дифференциальных косых формах, об основных свойствах, интегралах и классах пфаффовых систем, о геометрии линейной формы четкого и нечеткого классов. Отдельно дается материал по финслеровой геометрии и основной задаче вариационного исчисления. Рекомендуется специалистам — математикам и физикам, а...
Ставрополь: Мир данных, 2017. — 144 с. — ISBN: 978-5-91042-187-9. Монография посвящена теории нелинейных уравнений в частных производных для действительных и комплексных функций, обладающих операторной структурой. Найдена комплексификация иерархии уравнения Кортевега – де Вриза и иерархия возмущенного уравнения Кортевега – де Вриза с оператором рассеяния четвертого порядка....
Под ред. Э.Р. Розендорна. — Учебник для вузов. — 2-е изд., стереотип. — М.: Физматлит, 2017. — 336 с. — ISBN: 978-5-9221-1756-2. Теория уравнений с частными производными изложена в объеме, соответствующем программам математики для естественных факультетов университетов (кроме физических специальностей, у которых программа математики обширнее). Изложение сопровождается...
М.: Физматлит, 2014. — 304 с. — ISBN: 978-5-9221-1561-2. Монография посвящена изучению качественных и спектральных свойств решений уравнений и систем уравнений смешанного типа, в частности уравнения Чаплыгина, моделирующего плоскопараллельные околозвуковые течения. Представленные результаты имеют целью дальнейшую разработку метода принципа максимума, альтернирующего метода типа...
Монография. — Ташкент: Фан, 1974. — 156 с. В монографии рассматриваются краевые задачи для уравнениий смешанно-составного типа. Дается классификация таких уравнений и указываются канонические формы. Ставятся и исследуются краевые задачи для уравнений смешанно-составного типа третьего порядка с одной и двумя линиями вырождения как в ограниченной так и в неограниченной области....
Монография. — Ташкент, 2010. — 356 с. Монография посвящена постановке и исследованию задач на собственные значения для уравнений смешанного типа. В различных областях, состоящих из четвертей круга и характеристических треугольников, для уравнений смешанного типа наряду с обычным задачами сформулированы, новые задачи на собственные значения с нелокальными условиями, зависящими...
Харьков: Издание Харьковского математического общества, 1905. — 270 с. Образование производных уравнений С. Ли и задача их интегрирования. Свойства полных интегральных собраний С. Ли. Об интегрировании некоторых уравнений с частными производными первого порядка многих неизвестных функций. Разыскание производных уравнений С. Ли, допускающих полные интегралы С. Ли данного класса....
М.: Физматлит, 2007. — 737 с.
Рассматриваются проблемы глобальной и локальной разрешимости, как в классическом, так и в сильном и слабом обобщенном смыслах, широких классов задач Коши и начально-краевых задач для линейных и нелинейных уравнений в частных производных высоких порядков, включая псевдопараболические уравнения и уравнения Соболевского типа. В случае локальной...
К.: Наукова думка, 1973. — 221 с. В книге излагаются топологические методы исследования квазилинейных эллиптических уравнений высшего порядка и определенных классов нелинейных операторных уравнений в банаховых пространствах. Изучаются разрешимость граничных задач, задача о собственных значениях, свойства обобщенных решений квазилинейных эллиптических уравнений высшего порядка....
М.: Наука, 1964. — 208 с. Эта книга является пособием для студентов механико-математического и физико-математического факультетов вечерних и заочных отделений университетов. Она посвящена теории дифференциальных уравнений в частных производных второго порядка - тому разделу математики, который находит чрезвычайно широкое и многообразное применение в механике, физике и технике. В...
Монография. — М.: Высшая школа, 1966. — 344 с. Настоящая монография возникла в результате научно-исследовательской работы автора по теории особых решений уравнений с частными производными первого порядка. В книге рассматриваются особые решения уравнений в частных производных первого порядка и некоторые вопросы качественной теории этих уравнений. Она ставит ряд задач и вопросов,...
Учебное пособие. — М.: Московский государственный институт электроники и математики (МИЭМ), 1973. — 201 с. Предлагаемый текст представляет собой обработанные записки лекций, которые автор читал в качестве факультативного курса студентам старших курсов факультета прикладной математики. В предлагаемой работе рассматриваются квазиэллиптические уравнения в бесконечном цилиндре.
Монография. — Отв. ред. М.А. Шубин; АН СССР. — Новосибирск: Наука, Сибирское отделение, 1991. — 317 с. — ISBN 5-02-029324-5. Монография посвящена локальным вопросам теории уравнений с частными производными. Рассмотрены устранимые особенности решений систем дифференциальных уравнений, ряд Лорана для решений, равномерная аппроксимация и аппроксимация в среднем решениями...
Учебно-методическое пособие. — Владикавказ: Северо-Осетинский государственный университет (СОГУ), 2017. — 52 с. Основной целью данной работы является иллюстрация сочетания методов гармонического анализа и энергетического метода для решения граничных задач. Энергетический метод широко используется при решении качественных задач математической физики. В данной работе показано,...
Учебное пособие. — Новосибирск: Новосибирский государственный университет (НГУ), 1973. — 144 с. Спецкурс для студентов, специализирующихся в области дифференциальных уравнений, читаемый в НГУ. Основой этой книги является курс лекций, который автор читал в течение ряда лет аспирантам и студентам старших курсов матфака НГУ, по вырождающимся и смешанным дифференциальным уравнениям.
Пер. с англ. — М.: Мир, 1965. — 296 с. Книга посвящена общей теории дифференциальных уравнений в частных производных с постоянными коэффициентами. Главное внимание уделяется локальным свойствам решений, построению и исследованию различных фундаментальных решений, а также разрешимости «в целом». Дано обстоятельное введение в широкий круг современных исследований, в большой...
Учебное пособие. 2009. — 220 с. Учебное пособие по высшей математике по разделу дифференциальных уравнений. Задача Коши. Классификация линейных уравнений. Уравнения эллиптического типа. Уравнения гиперболического типа. Уравнения параболического типа. Метод возмущений. Уравнение Шредингера. Численные методы решения уравнений с частными производными. Интегральные уравнения....
Пер. с англ. — М.: Мир, 1985. — 384 с. Книга американского математика, представляющая собой учебное пособие по теории дифференциальных уравнений с частными производными. Она отличается компактностью, четкостью и наглядностью изложения и неформальным подходом в подаче материала. В ней много иллюстраций, графиков и диаграмм, вместо строгих доказательств часто приводятся...
Пер. с англ. — М.: Мир, 1968. — 428 с. Книга содержит обстоятельное и систематическое изложение теории уравнений параболического типа. В ней подробно освещаются многие проблемы, решенные лишь в последнее десятилетие. Общая теория параболических уравнений развивается до уровня, на котором читатель может без труда перейти к изучению периодической научной литературы. Автор уделяет...
Пер. с англ. Л.С. Франка. — Под ред. В.М. Борок и А.Г. Костюченко. — М.: Издательство иностранной литературы, 1959. — 71 с. — (Библиотека сборника "Математика"). В статье Ларса Хёрмандера изложен ряд глубоких и актуальных результатов в теории линейных уравнений с частными производными. В ней широко используются методы функционального анализа и, в частности, теории обобщенных...
М.: Грин Принт, 2019. — 180 с. Книга представляет собой учебник по современной теории дифференциальных уравнений в частных производных. Рассматриваются уравнения в пространствах Соболева, что отличает настоящий учебник от классического изложения уравнений в частных производных. Подробно со всеми доказательствами изложена теория пространств Соболева в ограниченных областях . Кроме...
Пер. с англ. Б.В. Карпова. — Под ред. А.Г. Кюркчана. — Москва: Техносфера, 2002. — 320 с. — (Мир математики). Основное содержание книги, посвященной методам и приемам решения уравнений в частных производных, дополнено главой по интегральным уравнениям. Отличительная черта пособия — необходимый минимум теоретического материала при множестве примеров, снабженных подробными...
Учебное пособие. — М.: АйПринт, 2018. — 58 с. Учебное пособие предназначено для проведения самостоятельной подготовки студентов по курсу «Уравнения в частных производных» или «Уравнения математической физики». В пособии рассмотрены следующие вопросы высшей математики: уравнения в частных производных первого порядка, уравнения в частных производных второго порядка, решение...
Учебное пособие. — М.: Московский государственный университет имени М.В. Ломоносова (МГУ), 1979. — 184 с. Основу книги составляет курс лекций, читаемый автором в течение ряда лет на физическом факультете МГУ. Книга содержит как классические основы теории — принцип максимума, теоремы существования, различные обобщенные решения, априорные оценки Шаудера, так и менее традиционный...
Уважаемые: администратор, модераторы и доверенные пользователи.Я сердечно благодарен Вам за создание подраздела Дифференциальные уравнения в частных производных. Теперь людям гораздо легче будет ориентироваться в разделе Дифференциальные уравнения и быстрее искать нужную литературу. Слава Богу! Да благословит Господь Вас, ваших родных, близких, друзей и знакомых. С уважением, благодарностью и благословением,
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Теперь людям гораздо легче будет ориентироваться в разделе Дифференциальные уравнения и быстрее искать нужную литературу. Слава Богу!
Да благословит Господь Вас, ваших родных, близких, друзей и знакомых.
С уважением, благодарностью и благословением,