Convergence of Approximate Solutions for Quasilinear Hyperbolic Conservation Laws with Relaxation

Abstract

In this article the author considers the limiting behavior of quasilinear hyperbolic conservation laws with relaxation, particularly the zero relaxation limit. Our analysis includes the construction of suitably entropy flux pairs to deduce the L∞ estimate of the solutions, and the theory of compensated compactness is then applied to study the convergence of the approximate solutions to its Cauchy problem.