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Hyperbolic conservation laws in continuum physics. 3rd ed. (English) Zbl 1196.35001
Grundlehren der Mathematischen Wissenschaften 325. Berlin: Springer (ISBN 978-3-642-04047-4/hbk; 978-3-642-04048-1/ebook). xxxv, 708 p. (2010).
This is the third edition of the famous book by C. M. Dafermos [Grundlehren der Mathematischen Wissenschaften. 325. Berlin: Springer (2000; Zbl 0940.35002), (2005; Zbl 1078.35001)] devoted to the mathematical theory of hyperbolic conservation and balance laws. This masterly written book is, surely, the most complete exposition in the subject of conservation laws.
New to the 3rd edition is a chapter recounting the exciting recent developments in classical open problems in compressible fluid flow. Still another addition is an account of the early history of the subject, spanning the period between 1800 to 1957. Furthermore, a substantial portion of the original text has been reorganized so as to streamline the exposition, update the information, and enrich the collection of applications. The bibliography, also expanded and updated, now comprises over fifteen hundred titles.

MSC:
35-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to partial differential equations
35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations
35L65 Hyperbolic conservation laws
35L67 Shocks and singularities for hyperbolic equations
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