Perturbations of Positive Semigroups with Applications

by Jacek Banasiak, Luisa Arlotti

Overview

Perturbations of Positive Semigroups with Applications is a self-contained introduction to semigroup theory with emphasis on positive semigroups on Banach lattices and perturbation techniques. The first part of the book presents a survey of the results that are needed for the second, applied part of the book; worked examples are provided to help absorb the theoretical material. The second part then deals with the application of the developed theory to a variety of problems ranging from the classical birth-and-death type problems of population dynamics, through fragmentation models in both conservative and mass loss regimes, to kinetic models.

The only prerequisites are a basic knowledge of functional analysis and measure theory. This is an essential one-stop reference for graduate and postgraduate students and researchers in applied analysis and mathematical physics who are interested in the application of functional analytic techniques to concrete problems arising in physics, biology and engineering.

Product Details

ISBN-13:	9781849969925
Publisher:	Springer London
Publication date:	10/21/2010
Series:	Springer Monographs in Mathematics
Edition description:	Softcover reprint of hardcover 1st ed. 2006
Pages:	438
Product dimensions:	6.10(w) x 9.25(h) x 0.04(d)

Table of Contents

Basic Facts from Functional Analysis and Banach Lattices.- An Overview of Semigroup Theory.- Some Classical Perturbation Results.- Positive Perturbations of Positive Semigroups.- Subshastic Semigroups and Generator Characterization.- Applications to Birth-and-death Problems.- Applications to Pure Fragmentation Problems.- Fragmentation with Growth and Decay.- Applications to Kinetic Theory.- Singularly Perturbed Inelastic Collision Models.

Editorial Reviews

From the reviews:

"Several books of different sorts have been devoted in recent years to semigroup theory applied to many types of problems. The book under review tries to answer some of the most important questions which arise in the above problems … . The references are very detailed … . the very accurate proofs of the theorems and the choices of the examples and applications make it quite readable. In my opinion, it is a very interesting and useful tool for both pure and applied mathematicians." (Silvia Totaro, Mathematical Reviews, Issue 2006 i)

"This book is a self-contained mathematical monograph devoted to the theory of semigroups of linear operators … . The book includes a systematic treatment of classical and recent results in this area as well as a comprehensive survey of the vast literature … . Each chapter contains a preliminary section with clear references to the bibliography and with technical remarks. … Throughout the book, the style is clear and elegant. … this book can be highly recommended to anybody who works in this area." (Adina Luminita Sasu, Zentralblatt MATH, Vol. 1097 (23), 2006)

"More precisely, as correctly described in the title, [BA] concentrates on the perturbation of positive semigroups and its applications to birth and death processes, fragmentation processes … and to kinetic theory. … Obviously [BA] should be in the hand of every researcher who is interested in any of these applications. It also seems to be the only book available that deals with relatively bounded positive perturbations of positive semigroups and with general questions of their shasticity and honesty." (H. R. Thieme, SIAM Review, Vol. 49 (2), 2007)

From the Publisher