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.
Author(s): Yong-kui Chang, Gaston Mandata N'guerekata, Rodrigo Ponce
Series: Series on Concrete and Applicable Mathematics
Publisher: World Scientific Publishing
Year: 2022
Language: English
Pages: 208
City: Singapore
Contents
Preface
About the Authors
Acknowledgments
1. Preliminaries
2. Bloch-Type Periodic Functions and Generalizations
2.1 Bloch-Type Periodic Functions
2.2 Pseudo Bloch-Type Periodic Functions
2.3 Weighted Pseudo Bloch-Type Periodic Functions
2.4 S-Class Asymptotically Bloch-Type Periodic Functions
2.5 Stepanov-Like Asymptotically Bloch-Type Periodic Functions
3. Bloch-Type Periodic Solutions to Semilinear Integrodifferential Equations of Mixed Kernel
3.1 Uniform Exponential Stability of Solutions to a Volterra Equation
3.2 Linear Integrodifferential Equation
3.3 Semilinear Integrodifferential Equation
4. Bloch-Type Periodic Solutions to Multi-Term Fractional Evolution Equations
4.1 Asymptotic Behavior and Uniform Integrability of the Resolvent Family
4.2 Linear Fractional Evolution Equation
4.3 Semilinear Fractional Evolution Equation
5. Bloch-Type Periodic Solutions to Fractional Evolution Equations of Sobolev Type
5.1 Asymptotic Behavior of Sobolev-Type Resolvent Family
5.2 Bloch-Type Periodic Solutions
6. Bloch-Type Periodic Solutions to Fractional Integrodifferential Equations
6.1 Fractional Integrodifferential Equation in the Linear Case
6.2 Fractional Integrodifferential Equation in the Semilinear Case
7. Asymptotically Bloch-Type Periodic Solutions to Damped Evolution Equations
7.1 Some Basic Results
7.2 Asymptotically Bloch-Type Periodic Solutions
8. Asymptotically Bloch-Type Periodic Solutions to Partial Integrodifferential Equations
8.1 Some Basic Results
8.2 Asymptotically Bloch-Type Periodic Solutions
9. Bloch-Type Periodic Solutions to Semilinear Integral Equations
9.1 Integral Resolvent Family and Linear Integral Equation
9.2 Semilinear Integral Equation
Appendix A Compactness of Fractional Resolvent Operator Families
A.1 Norm Continuity and Compactness of the Resolvent Operator Sα,β(t)
A.2 Norm Continuity and Compactness of the Resolvent Operator SEα,β(t)
A.3 Applications
Bibliography
Index
