Hyperbolic Conservation Laws in Continuum Physics

  • Constantine M.┬áDafermos

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

Table of contents

  1. Front Matter
    Pages I-XXXVIII
  2. Constantine M. Dafermos
    Pages 1-24
  3. Constantine M. Dafermos
    Pages 25-51
  4. Constantine M. Dafermos
    Pages 53-75
  5. Constantine M. Dafermos
    Pages 77-109
  6. Constantine M. Dafermos
    Pages 111-174
  7. Constantine M. Dafermos
    Pages 175-226
  8. Constantine M. Dafermos
    Pages 227-261
  9. Constantine M. Dafermos
    Pages 263-302
  10. Constantine M. Dafermos
    Pages 303-358
  11. Constantine M. Dafermos
    Pages 359-365
  12. Constantine M. Dafermos
    Pages 367-426
  13. Constantine M. Dafermos
    Pages 427-487
  14. Constantine M. Dafermos
    Pages 489-516
  15. Constantine M. Dafermos
    Pages 517-555
  16. Constantine M. Dafermos
    Pages 585-622
  17. Constantine M. Dafermos
    Pages 623-653
  18. Constantine M. Dafermos
    Pages 655-689
  19. Back Matter
    Pages 691-826

About this book


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.

This new edition places increased emphasis on hyperbolic systems of balance laws with dissipative source, modeling relaxation phenomena. It also presents an account of recent developments on the Euler equations of compressible gas dynamics. Furthermore, the presentation of a number of topics in the previous edition has been revised, expanded and brought up to date, and has been enriched with new applications to elasticity and differential geometry. The bibliography, also expanded and updated, now comprises close to two thousand titles.

From the reviews of the 3rd edition:

"This is the third edition of the famous book by C.M. Dafermos. His masterly written book is, surely, the most complete exposition in the subject." Evgeniy Panov, Zentralblatt MATH

"A monumental book encompassing all aspects of the mathematical theory of hyperbolic conservation laws, widely recognized as the "Bible" on the subject." Philippe G. LeFloch, Math. Reviews


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

Authors and affiliations

  • Constantine M.┬áDafermos
    • 1
  1. 1.Div. Applied MathematicsBrown UniversityPROVIDENCEUSA

Bibliographic information