# Hyperbolic Conservation Laws in Continuum Physics

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

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

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

- DOI https://doi.org/10.1007/978-3-662-49451-6
- Copyright Information Springer-Verlag Berlin Heidelberg 2016
- Publisher Name Springer, Berlin, Heidelberg
- eBook Packages Mathematics and Statistics
- Print ISBN 978-3-662-49449-3
- Online ISBN 978-3-662-49451-6
- Series Print ISSN 0072-7830
- Series Online ISSN 2196-9701
- About this book