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Hyperbolic and viscous conservation laws

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Here is an in-depth, up-to-date 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 is useful for the study of various physical situations, including nonlinear elasticity, magnetohydrodynamics, multiphase flows, combustion, and classical gas dynamics shocks. The central issue throughout the book is the understanding of nonlinear wave interactions.

The book describes the qualitative theory of shock waves. It begins with the basics of the theory for scalar conservation law and Lax's solution of the Reimann problem. For hyperbolic conservation laws, the Glimm scheme and wave tracing techniques are presented and used to study the regularity and large-time behavior of solutions. Viscous nonlinear waves are studied via the recent approach to pointwise estimates.

Author(s): Tai-Ping Liu
Series: CBMS-NSF regional conference series in applied mathematics 72
Publisher: Society for Industrial and Applied Mathematics
Year: 2000

Language: English
Pages: 84
City: Philadelphia
Tags: Математика;Дискретная математика;

Hyperbolic and Viscous Conservation Laws......Page 2
CBMS-NSF REGIONAL CONFERENCE SERIES IN APPLIED MATHEMATICS......Page 3
ISBN 0-89871-436-2......Page 7
Contents......Page 8
Preface......Page 10
1.1 Preliminaries......Page 12
1.2 Riemann Problem......Page 19
1.3 Wave Interactions......Page 27
1.4 Random Choice Method......Page 32
1.5 Nonlinear Superposition......Page 40
1.6 Large-Time Behavior and Regularity......Page 46
2.1 Preliminaries......Page 50
2.2 The Burgers Equation......Page 52
2.3 Diffusion Waves......Page 63
2.4 Viscous Shocks......Page 70
2.5 Viscous Rarefaction Waves......Page 79
2.6 Concluding Remarks......Page 80
Bibliography......Page 82
Index......Page 84