Relaxation limit of interacting shock waves for non-isentropic gas dynamics

In this paper, we study the relaxation limit of interacting shock waves for non-isentropic gas dynamics, such a model is introduced by Jin and Xin for numerical analysis and named as Jin-Xin relaxation system. Given any entropy solution of non-isentropic gas dynamics which consists of two different families of shocks interacting at some positive time, we show that such solution is the relaxation limit for a family of smooth global solutions of the Jin-Xin relaxation system. We remark that, after the interacting time, not only shocks but also contact discontinuity is generated.