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A Concise Guide to Semigroups and Evolution Equations cover

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 AG(1,0;X)
  • The Cases AG(M,β;X) and AG'(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.

Free Access
FRONT MATTER
  • Pages:i–xiii

https://doi.org/10.1142/9789814354554_fmatter

Free Access
TWO TYPICAL EVOLUTION PROBLEMS
  • Pages:1–13

https://doi.org/10.1142/9789814354554_0001

No Access
SEMIGROUPS GENERATED BY BOUNDED OPERATORS
  • Pages:14–34

https://doi.org/10.1142/9789814354554_0002

No Access
SEMIGROUPS GENERATED BY A ∈ G(1,0;X)
  • Pages:35–54

https://doi.org/10.1142/9789814354554_0003

No Access
THE CASES A ∈ G(M,βX) AND A ∈ G'(1,0;X)
  • Pages:55–68

https://doi.org/10.1142/9789814354554_0004

No Access
BOUNDED PERTURBATIONS
  • Pages:69–78

https://doi.org/10.1142/9789814354554_0005

No Access
HOLOMORPHIC SEMIGROUPS
  • Pages:79–95

https://doi.org/10.1142/9789814354554_0006

No Access
A LINEAR EVOLUTION PROBLEM
  • Pages:96–105

https://doi.org/10.1142/9789814354554_0007

No Access
SEMILINEAR EVOLUTION PROBLEMS
  • Pages:106–148

https://doi.org/10.1142/9789814354554_0008

Free Access
BACK MATTER
  • Pages:149–166

https://doi.org/10.1142/9789814354554_bmatter

“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.”

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.”

Mathematical Reviews