Hyperbolic conservation laws in continuum physics.
2nd ed.

*(English)*Zbl 1078.35001
Grundlehren der Mathematischen Wissenschaften 325. Berlin: Springer (ISBN 3-540-25452-8/hbk). xix, 626 p. (2005).

The second edition of the famous book Grundlehren der Mathematischen Wissenschaften 325 (Berlin: Springer) (2000; Zbl 0940.35002) is devoted to the mathematical theory of hyperbolic conservation and balance laws. The author is known as one of the leading experts in the field. His masterly written book is, surely, the most complete exposition in the subject of conservation laws. But in view of the explosive development of the theory of conservation laws it has become necessary to prepare a considerably revised and expanded second edition.

A new chapter has been added (Chapter XV) devoted to the vanishing viscosity method. Numerous new sections in preexisting chapters have been incorporated, to introduce newly derived results or present older material, omitted in the first edition. This includes recent not published work by the author. In addition, the original text has been reorganized so as to streamline the exposition, enrich the collection of examples, and improve the notation.

The bibliography has been considerably expanded, now comprising over one thousand titles.

A new chapter has been added (Chapter XV) devoted to the vanishing viscosity method. Numerous new sections in preexisting chapters have been incorporated, to introduce newly derived results or present older material, omitted in the first edition. This includes recent not published work by the author. In addition, the original text has been reorganized so as to streamline the exposition, enrich the collection of examples, and improve the notation.

The bibliography has been considerably expanded, now comprising over one thousand titles.

Reviewer: Evgeniy Panov (Novgorod)

##### 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 |