Stability of a superposition of shock waves with contact discontinuities   for the Jin-Xin relaxation system
  In this paper, we consider the large time asymptotic nonlinear stability of a superposition of shock waves with contact discontinuities for the one dimensional Jin-Xin relaxation system with small initial perturbations, provided that the strengths of waves are small with the same order. The results are obtained by elementary weighted energy estimates based on the underlying wave structure and an estimate on the heat equation. 
Hualin Zheng
math.AP