Series on Advances in Mathematics for Applied Sciences - Vol. 19
A CONCISE GUIDE TO SEMIGROUPS AND EVOLUTION EQUATIONS
by A Belleni-Morante (Univ. Firenze)
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).
Contents:
- Two Typical Evolution Problems
- Semigroups Generated by Bounded Operators
-
Semigroups Generated by A Î G(1,0,X)
- The Cases A Î G(M,b,X) and A Î 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.
“The present book is a nice, simple and concise introduction to the theory of one parameter semigroups of operators and their applications to evolution equations.”
A Rhandi
Mathematics Abstracts |
“This book is written in a clear and readily accessible way and can be recommended as good introductory reading on semigroup theory, in particular for non-mathematicians.”
Alexei I Filinkov
Mathematical Reviews |
| 180pp |
Pub. date: May 1994 |
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