Beyond Partial Differential Equations: On Linear and Quasi-Linear Abstract Hyperbolic Evolution Equations / Edition 1

by Horst Reinhard Beyer

Overview

This book introduces the treatment of linear and nonlinear (quasi-linear) abstract evolution equations by methods from the theory of strongly continuous semigroups. The theoretical part is accessible to graduate students with basic knowledge in functional analysis, with only some examples requiring more specialized knowledge from the spectral theory of linear, self-adjoint operators in Hilbert spaces. Emphasis is placed on equations of the hyperbolic type which are less often treated in the literature.

Product Details

ISBN-13:	9783540711285
Publisher:	Springer Berlin Heidelberg
Publication date:	05/18/2007
Series:	Lecture Notes in Mathematics , #1898
Edition description:	2007
Pages:	283
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

Conventions.- Mathematical Introduction.- Prerequisites.- Strongly Continuous Semigroups.- Examples of Generators of Strongly Continuous Semigroups.- Intertwining Relations, Operator Homomorphisms.- Examples of Constrained Systems.- Kernels, Chains, and Evolution Operators.- The Linear Evolution Equation.- Examples of Linear Evolution Equations.- The Quasi-Linear Evolution Equation.- Examples of Quasi-Linear Evolution Equations.

Editorial Reviews

From the reviews:

"In the monograph under review, designed as a textbook for graduate students, the author aims to build up the theory in a straightforward way in view of physical applications. … The material covered in the book was used in a two-semester course for graduate students. The book is a good summary of the most important facts of the theory of evolution equations, and is also a good source of information for researchers looking for new applications of this theory." (András Bátkai, Mathematical Reviews, Issue 2008 h)

"This well-written work is the outgrowth of a two-semester course on linear semigroup methods, linear and quasi-linear hyperbolic systems of partial differential equations, and the abstract theory of evolution equations … . Although the text was written for truly advanced graduate students, it contains a wealth of well presented results on semigroup theory of evolution equations … and will therefore serve as a valuable resource for researchers in mathematics and theoretical physics as well." (Thomas Hagen, Zentralblatt MATH, Vol. 1144, 2008)

From the Publisher