Asymptotic analysis of the Riemann problem for constant coefficient hyperbolic systems with relaxation

The discontinuous Riemann initial value problem is considered for dissipative, constant coefficient hyperbolic systems with relaxation source terms. A short-time asymptotic expansion, a specialization of the results of Le Floch and Raviart [11], is constructed for the general linear system. Exact rates for the decay of the initial discontinuities are found to be in agreement with recent results from other approaches. A multiple scales analysis is used to identify the long-time asymptotic behavior. Many of the results can be exemplified in a simple model problem for which the exact solution can be found.