Lecture Notes in Mathematics
cover

Beyond Partial Differential Equations

On Linear and Quasi-Linear 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
see more benefits

Buy this book

eBook n/a
  • ISBN 978-3-540-71129-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
Softcover n/a
  • ISBN 978-3-540-71128-5
  • with online files
  • Free shipping for individuals worldwide
About this book

The present volume is self-contained and introduces to 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. Only some examples require more specialized knowledge from the spectral theory of linear, self-adjoint 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 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)


Table of contents (12 chapters)

Table of contents (12 chapters)
  • Conventions

    Pages 1-3

  • Mathematical Introduction

    Pages 5-12

  • Prerequisites

    Pages 13-39

  • Strongly Continuous Semigroups

    Pages 41-69

  • Examples of Generators of Strongly Continuous Semigroups

    Pages 71-103

Buy this book

eBook n/a
  • ISBN 978-3-540-71129-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
Softcover n/a
  • ISBN 978-3-540-71128-5
  • with online files
  • Free shipping for individuals worldwide
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Beyond Partial Differential Equations
Book Subtitle
On Linear and Quasi-Linear Abstract Hyperbolic Evolution Equations
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1898
Copyright
2007
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-71129-2
DOI
10.1007/978-3-540-71129-2
Softcover ISBN
978-3-540-71128-5
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XIV, 283
Topics