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.

Contents:

• Preliminaries


• Bloch-Type Periodic Functions and Generalizations


• Bloch-Type Periodic Solutions to Semilinear Integrodifferential Equations of Mixed Kernel


• Bloch-Type Periodic Solutions to Multi-Term Fractional Evolution Equations


• Bloch-Type Periodic Solutions to Fractional Evolution Equations of Sobolev Type


• Bloch-Type Periodic Solutions to Fractional Integrodifferential Equations


• Asymptotically Bloch-Type Periodic Solutions to Damped Evolution Equations


• Asymptotically Bloch-Type Periodic Solutions to Partial Integrodifferential Equations


• Bloch-Type Periodic Solutions to Semilinear Integral Equations


• Appendix: Compactness of Fractional Resolvent Operator Families

Readership: This book is designed for graduate students and beginning researchers in harmonic analysis and long-term behavior of evolution equations. It can be used to conduct seminars on special topics at the graduate level.

Key Features:

• Showcases recent results on periodic functions of the Bloch-type


• Lays down both the foundation of the theory of periodic functions of the Bloch-type


• Applications of the theory of Bloch-type periodic functions to several evolution equations are presented


• This book may serve as a reference text for graduate seminars. It is useful to researchers and graduate students in the mathematics, science, and engineering