Overview
Contains new results on semilinear evolution equations
Features extensive references to the related literature
Presents recent trends and developments in a self-contained way
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Table of contents (10 chapters)
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Front Matter
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Back Matter
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
About this book
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.
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Authors and Affiliations
Bibliographic Information
Book Title: Semilinear Evolution Equations and Their Applications
Authors: Toka Diagana
DOI: https://doi.org/10.1007/978-3-030-00449-1
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2018
Hardcover ISBN: 978-3-030-00448-4Published: 03 November 2018
Softcover ISBN: 978-3-030-13114-2Published: 10 December 2019
eBook ISBN: 978-3-030-00449-1Published: 23 October 2018
Edition Number: 1
Number of Pages: XX, 189
Topics: Functional Analysis, Operator Theory, Partial Differential Equations, Difference and Functional Equations