This book is a simple and concise introduction to the theory of semigroups and evolution equations, both in the linear and in the semilinear case. The subject is presented by a discussion of two standard boundary value problems (from particle transport theory and from population theory), and by showing how such problems can be rewritten as evolution problems in suitable Banach spaces.
Each section of the book is completed by some notes, where the relevant notions of functional analysis are explained. Some other definitions and theorems of functional analysis are discussed in the Appendices (so that the only prerequisites to read the book are classical differential and integral calculus).
Sample Chapter(s)
Chapter 1: Two Typical Evolution Problems (1,041 KB)
Contents:
- Two Typical Evolution Problems
- Semigroups Generated by Bounded Operators
- Semigroups Generated by A ∈ G(1,0;X)
- The Cases A ∈ G(M,β;X) and A ∈ G'(1,0;X)
- Bounded Perturbations
- Holomorphic Semigroups
- A Linear Evolution Problem
- Semilinear Evolution Problems
- Lebesgue Measure and Lebesgue Integral
- Banach Spaces
- References
- Subject Index
Readership: Undergraduates and graduates in mathematics, physics and engineering.
