Hyperbolic Conservation Laws in Continuum Physics

  • Constantine M.┬áDafermos

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 325)

Table of contents

  1. Front Matter
    Pages i-xxxv
  2. Constantine M. Dafermos
    Pages 1-24
  3. Constantine M. Dafermos
    Pages 25-51
  4. Constantine M. Dafermos
    Pages 53-74
  5. Constantine M. Dafermos
    Pages 75-96
  6. Constantine M. Dafermos
    Pages 97-144
  7. Constantine M. Dafermos
    Pages 145-194
  8. Constantine M. Dafermos
    Pages 195-229
  9. Constantine M. Dafermos
    Pages 231-269
  10. Constantine M. Dafermos
    Pages 271-324
  11. Constantine M. Dafermos
    Pages 325-330
  12. Constantine M. Dafermos
    Pages 331-372
  13. Constantine M. Dafermos
    Pages 373-433
  14. Constantine M. Dafermos
    Pages 435-475
  15. Constantine M. Dafermos
    Pages 477-515
  16. Constantine M. Dafermos
    Pages 545-571
  17. Constantine M. Dafermos
    Pages 573-596
  18. Back Matter
    Pages 597-708

About this book

Introduction

This is a masterly exposition and an encyclopedic presentation of the theory of hyperbolic conservation laws. It illustrates the essential role of continuum thermodynamics in providing motivation and direction for the development of the mathematical theory while also serving as the principal source of applications. The reader is expected to have a certain mathematical sophistication and to be familiar with (at least) the rudiments of analysis and the qualitative theory of partial differential equations, whereas prior exposure to continuum physics is not required. The target group of readers would consist of
(a) experts in the mathematical theory of hyperbolic systems of conservation laws who wish to learn about the connection with classical physics;
(b) specialists in continuum mechanics who may need analytical tools;
(c) experts in numerical analysis who wish to learn the underlying mathematical theory; and
(d) analysts and graduate students who seek introduction to the theory of hyperbolic systems of conservation laws.

New to the 3rd edition is an account of the early history of the subject, spanning the period between 1800 to 1957. Also new is a chapter recounting the recent solution of open problems of long standing in classical aerodynamics. Furthermore, the presentation of a number of topics in the previous edition has been revised and brought up to date, and the collection of applications has been substantially enriched. The bibliography, also expanded and updated, now comprises over fifteen hundred titles.

From the reviews of the 2nd edition:

"The author is known as one of the leading experts in the field. His masterly written book is, surely, the most complete exposition in the subject." Evgeniy Panov, Zentralblatt MATH

"This book is sure to convince every reader that working in this area is challenging, enlightening, and joyful." Katarina Jegdic, SIAM Review

Keywords

aerodynamics conservation laws continuum mechanics hyperbolic systems mechanics partial differential equations shock waves stability thermodynamics

Authors and affiliations

  • Constantine M.┬áDafermos
    • 1
  1. 1.Div. Applied MathematicsBrown UniversityProvidenceU.S.A.

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-04048-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 2010
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-04047-4
  • Online ISBN 978-3-642-04048-1
  • Series Print ISSN 0072-7830
  • About this book