Convergence of a Relaxation Scheme for a 2×2 Triangular System of Conservation Laws

Abstract

We study relaxation approximations to solutions of a 2 × 2 triangular system of conservation laws. We show that smooth relaxation approximations exist for all time. A finite difference approximation of the relaxation system gives rise to a relaxation scheme of the Jin and Xin type. In both cases we show that a sequence of approximate solutions is produced where the limit is a weak solution of the triangular system. Compensated compactness is used to establish convergence.