Liu Tai-Ping. Hyperbolic and Viscous Conservation Laws

Society for Industrial Mathematics, 2000. 84 p.
ISBN10: 0898714362Here 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.Hyperbolic Conservation Laws
Preliminaries
Riemann Problem
Wave Interactions
Random Choice Method
Nonlinear Superposition
Large-Time Behavior and Regularity
Viscous Conservation Laws
Preliminaries
The Burgers Equation
Diffusion Waves
Viscous Shocks
Viscous Rarefaction Waves
Concluding Remarks