© 2000

Hyperbolic Conservation Laws in Continuum Physics

  • The author is unquestionably the greatest authority on the subject as well as a masterly writer

  • The book will immediately find a following as both an introduction to the field and a reference for research


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

Table of contents

  1. Front Matter
    Pages I-XVI
  2. Constantine M. Dafermos
    Pages 1-18
  3. Constantine M. Dafermos
    Pages 19-35
  4. Constantine M. Dafermos
    Pages 37-47
  5. Constantine M. Dafermos
    Pages 49-60
  6. Constantine M. Dafermos
    Pages 61-82
  7. Constantine M. Dafermos
    Pages 83-119
  8. Constantine M. Dafermos
    Pages 121-145
  9. Constantine M. Dafermos
    Pages 147-174
  10. Constantine M. Dafermos
    Pages 175-202
  11. Constantine M. Dafermos
    Pages 203-208
  12. Constantine M. Dafermos
    Pages 209-237
  13. Constantine M. Dafermos
    Pages 239-297
  14. Constantine M. Dafermos
    Pages 299-335
  15. Constantine M. Dafermos
    Pages 337-369
  16. Constantine M. Dafermos
    Pages 371-395
  17. Back Matter
    Pages 397-446

About this book


The seeds of Continuum Physics were planted with the works of the natural philosophers of the eighteenth century, most notably Euler; by the mid-nineteenth century, the trees were fully grown and ready to yield fruit. It was in this envi­ ronment that the study of gas dynamics gave birth to the theory of quasilinear hyperbolic systems in divergence form, commonly called "hyperbolic conserva­ tion laws"; and these two subjects have been traveling hand-in-hand over the past one hundred and fifty years. This book aims at presenting the theory of hyper­ bolic conservation laws from the standpoint of its genetic relation to Continuum Physics. Even though research is still marching at a brisk pace, both fields have attained by now the degree of maturity that would warrant the writing of such an exposition. In the realm of Continuum Physics, material bodies are realized as continuous media, and so-called "extensive quantities", such as mass, momentum and energy, are monitored through the fields of their densities, which are related by balance laws and constitutive equations. A self-contained, though skeletal, introduction to this branch of classical physics is presented in Chapter II. The reader may flesh it out with the help of a specialized text on the subject.


Boundary value problem Entropy hyperbolic conservation laws partial differential equation partial differential equations thermodynamics

Authors and affiliations

  1. 1.Division of Applied MathematicsBrown UniversityProvidenceUSA

Bibliographic information

  • Book Title Hyperbolic Conservation Laws in Continuum Physics
  • Authors Constantine M. Dafermos
  • Series Title Grundlehren der mathematischen Wissenschaften
  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2000
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-3-540-64914-4
  • Softcover ISBN 978-3-662-22021-4
  • eBook ISBN 978-3-662-22019-1
  • Series ISSN 0072-7830
  • Edition Number 1
  • Number of Pages XVI, 446
  • Number of Illustrations 5 b/w illustrations, 0 illustrations in colour
  • Topics Partial Differential Equations
    Classical Mechanics
  • Buy this book on publisher's site
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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)