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Hyperbolic Conservation Laws in Continuum Physics

Hyperbolic Conservation Laws in Continuum Physics by Constantine M. Dafermos
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This is a masterly exposition and an encyclopedicpresentation of the theory of hyperbolic conservation laws. It illustrates theessential role of continuum thermodynamics in providing motivation anddirection for the development of the mathematical theory while also serving asthe principal source of applications. The reader is expected to have a certainmathematical sophistication and to be familiar with (at least) the rudiments ofanalysis and the qualitative theory of partial differential equations, whereasprior exposure to continuum physics is not required. The target group ofreaders would consist of 
(a) experts in the mathematical theory of hyperbolic systems of conservationlaws 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 mathematicaltheory; and 
(d) analysts and graduate students who seek introduction to the theory ofhyperbolic systems of conservation laws.

This new edition places increased emphasis onhyperbolic systems of balance laws with dissipative source, modeling relaxationphenomena. It also presents an account of recent developments on the Eulerequations of compressible gas dynamics. Furthermore, the presentation of anumber of topics in the previous edition has been revised, expanded andbrought up to date, and has been enriched with new applications toelasticity and differential geometry. The bibliography, also expanded andupdated, now comprises close to two thousand titles.

From the reviews of the 3rd edition:

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

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

Springer Berlin Heidelberg; May 2016
852 pages; ISBN 9783662494516
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Title: Hyperbolic Conservation Laws in Continuum Physics
Author: Constantine M. Dafermos
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