Authors:
- Written by an author who is unquestionably an authority on the subject as well as a masterly writer
- Revised, up-to-date fourth edition includes new material on the Euler equations of gas dynamics, and on hyperbolic balance laws with dissipative source, as well as new applications to elasticity and differential geometry
- Features an expanded bibliography that now comprises close to two thousand titles
- Includes supplementary material: sn.pub/extras
Part of the book series: Grundlehren der mathematischen Wissenschaften (GL)
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Table of contents (18 chapters)
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Front Matter
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Back Matter
About this book
OLD TEXT 4th Edition to be replaced: 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
Reviews
Authors and Affiliations
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Div. Applied Mathematics, Brown University, PROVIDENCE, USA
Constantine M. Dafermos
About the author
In addition to several honorary degrees, he has received the SIAM W.T. and Idalia Reid Prize (2000), the Cataldo e Angiola Agostinelli Prize of the Accademia Nazionale dei Lincei (2011), the Galileo Medal of the City of Padua (2012), and the Prize of the International Society for the Interaction of Mechanics and Mathematics (2014). He was elected a Fellow of SIAM (2009) and a Fellow of the AMS (2013). In 2016 he received the Wiener Prize, awarded jointly by the American Mathematical Society (AMS) and the Society for Industrial and Applied Mathematics (SIAM).
Bibliographic Information
Book Title: Hyperbolic Conservation Laws in Continuum Physics
Authors: Constantine M. Dafermos
Series Title: Grundlehren der mathematischen Wissenschaften
DOI: https://doi.org/10.1007/978-3-662-49451-6
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2016
Hardcover ISBN: 978-3-662-49449-3Published: 06 June 2016
Softcover ISBN: 978-3-662-57011-1Published: 30 May 2018
eBook ISBN: 978-3-662-49451-6Published: 26 May 2016
Series ISSN: 0072-7830
Series E-ISSN: 2196-9701
Edition Number: 4
Number of Pages: XXXVIII, 826
Number of Illustrations: 52 b/w illustrations
Topics: Partial Differential Equations, Thermodynamics, Classical Mechanics, Solid Mechanics, Fluid- and Aerodynamics
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