Hyperbolic conservation laws in continuum physics
著者
書誌事項
Hyperbolic conservation laws in continuum physics
（Die Grundlehren der mathematischen Wissenschaften, 325）
Springer, c2000
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注記
Bibliography: p. [397]-433
Includes indexes
内容説明・目次
内容説明
This masterly exposition of the mathematical theory of hyperbolic system laws brings out the intimate connection with continuum thermodynamics, emphasizing issues in which the analysis may reveal something about the physics and, in return, the underlying physical structure may direct and drive the analysis. The reader should have a certain mathematical sophistication and be familiar with (at least) the rudiments of the qualitative theory of PDE, whereas the required notions from continuum physics are introduced from scratch. The target group of readers would consist of (a) experts in the mathematical theory of hyperbolic systems of conservation laws who wish to learn about the connection with classical physics; (b) specialists in continuum mechanics; (c) experts in numerical analysis who wish to learn the underlying mathematical theory; and (d) analysts and graduate students who seek introduction to the theory of hyperbolic systems of conservation laws."
目次
Balance Laws * Introduction to Continuum Physics * Hyperbolic Systems of Balance Laws * The Initial-Value Problem: Admissibility of Solutions * Entropy and the Stability of Classical Solutions * The L1 Theory of Scalar Balance Laws * Hyperbolic Systems of Balance Laws in One Space Dimension * Admissible Shocks * Admissible Wave Fans and the Riemann Problem * Generalized Characteristics * Genuinely Nonlinear Scalar Conservation Law * Genuinely Nonlinear Systems of Two Conservation Laws * The Random Choice Method * The Method of Wave Front Tracking and the Standard Riemann Semigroup * The Method of Compensated Compactness * Bibliography.
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