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Hyperbolic conservation laws in continuum physics. 4th edition. (English) Zbl 1364.35003
Grundlehren der Mathematischen Wissenschaften 325. Berlin: Springer (ISBN 978-3-662-49449-3/hbk; 978-3-662-49451-6/ebook). xxxviii, 826 p. (2016).
The book presents a broad overview of the theory of hyperbolic conservation laws and their application to continuum physics. The author begins from the basics, giving self-contained introduction into theories of balance equations and different branches of continuum physics, including thermoelasticity, thermomechanics, etc. Most chapters are devoted to problems with one spatial variable. Much attention is paid to relaxation phenomena, i.e., presence of a dissipative force. Although the author declares moderation of encyclopedic ambitions in the fourth edition of the book due to explosive growth of research in the area, the book describes, at least briefly, most topics that deal with hyperbolic conservation laws.
For editions one to three, see [Zbl 0940.35002], [Zbl 1078.35001] and [Zbl 1196.35001].

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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