The Jin–Xin relaxation approximation of scalar conservation laws in several dimensions with large initial perturbation

Abstract

This paper is concerned with nonlinear stability of strong planar rarefaction waves for the Jin–Xin relaxation approximation of scalar conservation laws in several dimensions. For such a problem, local stability of weak or strong planar rarefaction waves have been obtained in Luo (1997) [20] and Zhao (2000) [43] respectively. For the global stability results, to the best of our knowledge, the only result available now is on the one-dimensional case, cf. Zhao (2000) [43], which is based on the maximum principle established in Natalini (1996) [30]. The main purpose of this paper is try to deduce some nonlinear stability results with large initial perturbation. Our analysis is based on the elementary energy method and the continuation argument.