Hyperbolic and Viscous Conservation Laws

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.