The Broadwell Model Contains The Asymptotic Stability Of The Viscous Shock Wave And The Viscous Contact Discontinuous Solution

We are concerned with the large-time behavior of solutions of the Cauchy problem to the Broadwell model system .When the Riemann prob-lem for the corresponding conservation Laws admits the solution consisting of contact discontinuity and shock waves, we prove that for the Broadwell model system, the combination wave of the contact discontinuity, and shock waves is asymptotically stable, provided the strength of the combi-nation wave is suitably small. This result is proved by using elementary energy methods.