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Semilinear Evolution Equations and Their Applications

  • Toka Diagana

Table of contents

  1. Front Matter
    Pages i-xx
  2. Toka Diagana
    Pages 1-28
  3. Toka Diagana
    Pages 29-43
  4. Toka Diagana
    Pages 45-56
  5. Toka Diagana
    Pages 57-74
  6. Toka Diagana
    Pages 75-83
  7. Toka Diagana
    Pages 85-95
  8. Toka Diagana
    Pages 97-111
  9. Toka Diagana
    Pages 113-124
  10. Toka Diagana
    Pages 125-138
  11. Toka Diagana
    Pages 139-176
  12. Back Matter
    Pages 177-189

About this book

Introduction

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 are established using various tools from nonlinear functional analysis and operator theory (such as semigroup methods). Various applications to partial differential equations and the dynamic of populations are amply discussed. 

This self-contained volume is primarily intended for advanced undergraduate and graduate students, post-graduates and researchers, but may also be of interest to non-mathematicians such as physicists and theoretically oriented engineers. It can also be used as a graduate text on evolution equations and difference equations and their applications to partial differential equations and practical problems arising in population dynamics. For completeness, detailed preliminary background on Banach and Hilbert spaces, operator theory, semigroups of operators, and almost periodic functions and their spectral theory are included as well.


Keywords

semilinear equation Hilbert space Banach space Sobolev space semigroup of operator difference equation singular difference equation degenerate evolution equation fractional differential equation heat equation Beverton-Holt dumping exponentially stable mild solution strong solution generalized solution weak solution Banach fixed point theorem Schauder fixed point theorem resolvent

Authors and affiliations

  • Toka Diagana
    • 1
  1. 1.Department of Mathematical SciencesUniversity of Alabama in HuntsvilleHuntsvilleUSA

Bibliographic information