Hyperbolic Conservation Laws in Continuum Physics

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This masterly exposition presents an encyclopedic overview of hyperbolic conservation laws, highlighting the crucial role of continuum thermodynamics in shaping the mathematical theory and its applications. Readers should possess a certain level of mathematical sophistication, particularly in analysis and the qualitative theory of partial differential equations, though prior knowledge of continuum physics is not necessary. The intended audience includes experts in hyperbolic systems of conservation laws seeking connections to classical physics, continuum mechanics specialists needing analytical tools, numerical analysts interested in the underlying mathematical theory, and graduate students looking for an introduction to these systems. The new edition emphasizes hyperbolic systems of balance laws with dissipative sources, modeling relaxation phenomena, and includes recent developments concerning the Euler equations of compressible gas dynamics. Numerous topics from the previous edition have been revised, expanded, and updated, with new applications in elasticity and differential geometry. The bibliography has also been significantly enhanced, now featuring nearly two thousand titles. Reviews of the previous edition praised it as a comprehensive and authoritative resource on the subject.