Grundlehren der mathematischen Wissenschaften

Hyperbolic Conservation Laws in Continuum Physics

Authors: Dafermos, Constantine M.

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About this book

This masterly exposition of the mathematical theory of hyperbolic system for conservation laws brings out the intimate connection with continuum thermodynamics, by emphasising issues in which the analysis may reveal something about the physics and, in return, the underlying physical structure may direct and drive the analysis. The reader is expected to have a certain mathematical sophistication and to be familiar with (at least) the rudiments of the qualitative theory of partial differential equations, whereas the required notions from continuum physics are introduced from scratch. 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.

The 2nd edition contains a new chapter recounting the exciting recent developments on the vanishing viscosity method. Numerous new sections have been incorporated in preexisting chapters, to introduce newly derived results or present older material, omitted in the first edition, whose relevance and importance has been underscored by current trends in research. In addition, a substantal portion of the original text has been revamped so as to streamline the exposition, enrich the collection of examples and improve the notation. The bibliography has been updated and expanded as well, now comprising over one thousand titles.

 

Reviews

From the reviews of the second edition:

"The second edition of the famous book Grundlehren der Mathematischen Wissenschaften 325 is devoted to the mathematical theory of hyperbolic conservation and balance laws. 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 of conservations laws. … the original text has been reorganized so as to streamline the exposition, enrich the collection of examples, and improve the notation. … The bibliography has been considerably expanded … ." (Evgeniy Panov, Zentralblatt MATH, Vol. 1078, 2006)

"This comprehensive book is about rigorous mathematical theory of balance and conservation laws … . The statements of theorems are carefully and precisely written. The proofs are canonical and illuminating … . This book is sure to convince every reader that working in this area is challenging, enlightening, and joyful. I heartily recommend this book to anyone who wants to learn about the foundations of the theory of balance and conservation laws and their generic relations to continuum physics … ." (Katarina Jegdic, SIAM Review, Vol. 48 (3), 2006)


Table of contents (16 chapters)

Table of contents (16 chapters)
  • Balance Laws

    Pages 1-23

  • Introduction to Continuum Physics

    Pages 25-49

  • Hyperbolic Systems of Balance Laws

    Pages 51-66

  • The Cauchy Problem

    Pages 67-86

  • Entropy and the Stability of Classical Solutions

    Pages 87-122

Buy this book

eBook $99.00
price for USA in USD (gross)
  • ISBN 978-3-540-29089-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
Hyperbolic Conservation Laws in Continuum Physics
Authors
Series Title
Grundlehren der mathematischen Wissenschaften
Series Volume
325
Copyright
2005
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-29089-6
DOI
10.1007/3-540-29089-3
Series ISSN
0072-7830
Edition Number
2
Number of Pages
XX, 626
Number of Illustrations
39 b/w illustrations
Topics