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Hyperbolic conservation laws in continuum physics

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Constantine M. Dafermos

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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 solid mathematical background, 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 interested in their connection to classical physics, specialists in continuum mechanics seeking analytical tools, numerical analysts wanting to understand 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 related to the Euler equations of compressible gas dynamics. Many topics from the previous edition have been revised and updated, with new applications in elasticity and differential geometry. The bibliography has been expanded to nearly two thousand titles. Reviews of the previous edition praised it as a comprehensive and monumental work in the field, solidifying its status as a definitive resource on hyperbolic conservation laws.