Yong-kui Chang, N'guerekata G.M., Ponce R. Bloch-type Periodic Functions: Theory And Applications To Evolution Equations

Singapore: World Scientific Publishing, 2022. — 209 p.This monograph aims to provide for the first time a unified and homogenous presentation of the recent works on the theory of Bloch periodic functions, their generalizations, and their applications to evolution equations. It is useful for graduate students and beginning researchers as seminar topics, graduate courses and reference text in pure and applied mathematics, physics, and engineering.About the AuthorsPreliminaries
Bloch-Type Periodic Functions and Generalizations
Bloch-Type Periodic Functions
Pseudo Bloch-Type Periodic Functions
Weighted Pseudo Bloch-Type Periodic Functions
S-Class Asymptotically Bloch-Type Periodic Functions
Stepanov-Like Asymptotically Bloch-Type Periodic Functions
Bloch-Type Periodic Solutions to Semilinear Integrodifferential Equations of Mixed Kernel
Uniform Exponential Stability of Solutions to a Volterra Equation
Linear Integrodifferential Equation
Semilinear Integrodifferential Equation
Bloch-Type Periodic Solutions to Multi-Term Fractional Evolution Equations
Asymptotic Behavior and Uniform Integrability of the Resolvent Family
Linear Fractional Evolution Equation
Semilinear Fractional Evolution Equation
Bloch-Type Periodic Solutions to Fractional Evolution Equations of Sobolev Type
Asymptotic Behavior of Sobolev-Type Resolvent Family
Bloch-Type Periodic Solutions
Bloch-Type Periodic Solutions to Fractional Integrodifferential Equations
Fractional Integrodifferential Equation in the Linear Case
Fractional Integrodifferential Equation in the Semilinear Case
Asymptotically Bloch-Type Periodic Solutions to Damped Evolution Equations
Some Basic Results
Asymptotically Bloch-Type Periodic Solutions
Asymptotically Bloch-Type Periodic Solutions to Partial Integrodifferential Equations
Some Basic Results
Asymptotically Bloch-Type Periodic Solutions
Bloch-Type Periodic Solutions to Semilinear Integral Equations
Integral Resolvent Family and Linear Integral Equation
Semilinear Integral Equation
Appendix: Compactness of Fractional Resolvent Operator Families
Norm Continuity and Compactness of the Resolvent Operator Sα,β(t)
Norm Continuity and Compactness of the Resolvent Operator SEα,β(t)
Applications