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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

- Series:
**Grundlehren der mathematischen Wissenschaften** - Author:
**Constantine M. Dafermos (auth.)** - Year:
**2016** - Publisher:
**Springer-Verlag Berlin Heidelberg** - Language:
**English** - ISBN:
**978-3-662-49449-3, 978-3-662-49451-6**

- File size:
**6 873 923** - Format:
**pdf**

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Hyperbolic conservation laws are central in the theory of nonlinear partial differential equations, and in many applications in science and technology. In this book the reader is given a detailed, rigorous, and self-contained presentation of the theory of...

The area of nonstrictly hyperbolic conservation laws is emerging as an important field, not only because it developed from applications of current interest, such as reservoir simulation, visco-elasticity, and multiphase flow, but also because the subj...

This masterly exposition of the mathematical theory of hyperbolic system laws brings out the intimate connection with continuum thermodynamics, emphasizing issues in which the analysis may reveal something about the physics and, in return, the underlying ...

This masterly exposition of the mathematical theory of hyperbolic system laws brings out the intimate connection with continuum thermodynamics, emphasizing issues in which the analysis may reveal something about the physics and, in return, the underlying ...

Here is an in-depth, up-to-date analysis of wave interactions for general systems of hyperbolic and viscous conservation laws. This self-contained study of shock waves explains the new wave phenomena from both a physical and a mathematical standpoint....

This book is devoted to finite volume methods for hyperbolic systems of conservation laws. The accent is put on the development of tools for analyzing the nonlinear stability of Godunov schemes. Starting from theoretical considerations, the schemes are de...

Systems of conservation laws arise naturally in physics and chemistry. To understand them and their consequences (shock waves, finite velocity wave propagation) properly in mathematical terms requires, however, knowledge of a broad range of topics. This b...

Conservation Laws. Physics textbook. Contains chapter 1 - Conservation of Energy, chapter 2 - Simplifying the Energy Zoo, chapter 3 - Work: The Transfer of Mechanical Energy, chapter 4 - Conservation of Momentum, chapter 5 - Conservation of Angular Moment...

In 1915 Emmy Noether was invited by Klein and Hilbert to GĂ¶ttingen to assist them in understanding the law of conservation of energy in Einsteinâ€™s new general theory of relativity. She succeeded brilliantly. In the Invariante Variationsprobleme, published...

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