Semilinear Evolution Equations and Their Applications

Description

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. Front Matter ....Pages i-xx Banach and Hilbert Spaces (Toka Diagana)....Pages 1-28 Operator Theory (Toka Diagana)....Pages 29-43 Semi-Group of Linear Operators (Toka Diagana)....Pages 45-56 Almost Periodic Functions and Sequences (Toka Diagana)....Pages 57-74 Nonautonomous Difference Equations (Toka Diagana)....Pages 75-83 Singular Difference Equations (Toka Diagana)....Pages 85-95 Fractional Integro-Differential Equations (Toka Diagana)....Pages 97-111 First-Order Semilinear Evolution Equations (Toka Diagana)....Pages 113-124 Semilinear Fractional Evolution Equations (Toka Diagana)....Pages 125-138 Second-Order Semilinear Evolution Equations (Toka Diagana)....Pages 139-176 Back Matter ....Pages 177-189