Beyond Partial Differential Equations
On Linear and QuasiLinear Abstract Hyperbolic Evolution Equations
Authors: Beyer, Horst Reinhard
 Theory is accessible, with only some examples requiring more than basic graduate knowledge of functional analysis
 Emphasizes equations of the hyperbolic type, which are less often treated in the literature
 Also of interest to readers from theoretical physics
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 About this book

The present volume is selfcontained and introduces to the treatment of linear and nonlinear (quasilinear) 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. Only some examples require more specialized knowledge from the spectral theory of linear, selfadjoint operators in Hilbert spaces. Particular stress is on equations of the hyperbolic type since considerably less often treated in the literature. Also, evolution equations from fundamental physics need to be compatible with the theory of special relativity and therefore are of hyperbolic type. Throughout, detailed applications are given to hyperbolic partial differential equations occurring in problems of current theoretical physics, in particular to Hermitian hyperbolic systems. This volume is thus also of interest to readers from theoretical physics.
 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 twosemester 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 wellwritten work is the outgrowth of a twosemester course on linear semigroup methods, linear and quasilinear 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)
 Table of contents (12 chapters)


Conventions
Pages 13

Mathematical Introduction
Pages 512

Prerequisites
Pages 1339

Strongly Continuous Semigroups
Pages 4169

Examples of Generators of Strongly Continuous Semigroups
Pages 71103

Table of contents (12 chapters)
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Bibliographic Information
 Bibliographic Information

 Book Title
 Beyond Partial Differential Equations
 Book Subtitle
 On Linear and QuasiLinear Abstract Hyperbolic Evolution Equations
 Authors

 Horst Reinhard Beyer
 Series Title
 Lecture Notes in Mathematics
 Series Volume
 1898
 Copyright
 2007
 Publisher
 SpringerVerlag Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
 eBook ISBN
 9783540711292
 DOI
 10.1007/9783540711292
 Softcover ISBN
 9783540711285
 Series ISSN
 00758434
 Edition Number
 1
 Number of Pages
 XIV, 283
 Topics