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9780898714364 Academic Inspection Copy

Hyperbolic and Viscous Conservation Laws

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An analysis of wave interactions for general systems of hyperbolic and viscous conservation laws. This self-contained study of shock waves explains the new wave phenomena from both a physical and a mathematical standpoint. The analysis should be useful for the study of various physical situations, including nonlinear elasticity, magneto-hydrodynamics, multi-phase flows, combustion, and classical gas dynamics shocks. The central issue throughout is the understanding of nonlinear wave interactions. The book describes the qualitative theory of shock waves. It starts with the basics of the theory for scalar conservation law and Lax's solution of the Riemann problem. For hyperbolic conservation laws, Glimm scheme and wave tracing techniques are presented and used to study the regularity and large-time behaviour of solutions. Viscous nonlinear waves are studied by the approach of point estimates.
Preface Chapter 1: Hyperbolic Conservation Laws. Preliminaries Riemann Problem Wave Interactions Random Choice Method Nonlinear Superposition Large-Time Behavior and Regularity Chapter 2: Viscous Conservation Laws. Preliminaries Burgers Equation Diffusion Waves Viscous Shocks Viscous Rarefaction Waves Concluding Remarks Bibliography Index
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