Stability of Riemann solutions to a class of non-strictly hyperbolic systems of conservation laws

Abstract

This paper is concerned with Riemann problem for a class of non-strictly hyperbolic systems of conservation laws. The two kinds of  Riemann solutions including vacuum and delta shock wave are constructed. Under the generalized RankineHugoniot relation and  entropy condition, we establish the existence and uniqueness of delta shock wave solutions. Furthermore, by studying the interactions  among of the delta shock wave and vacuum as well as contact discontinuity, the Riemann solutions with four kinds of different structures  are obtained. Additionally, the stability of the Riemann solutions is obtained under certain perturbation of the initial data.