Stability of contact discontinuity for Jin–Xin relaxation system

In this paper, we first construct a contact wave for 1-dimensional Jin–Xin relaxation system [S. Jin, Z.P. Xin, The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Comm. Pure Appl. Math. 48 (1995) 235–277]. This wave serves as the relaxation version of contact discontinuity of the corresponding hyperbolic system at equilibrium. Such a contact wave is shown to be nonlinearly stable under small initial perturbation. The time-decay rate is also obtained by weighted energy estimates.