A global asymptotic expansion for the solution to the generalized Riemann problem

Abstract

We study the generalized Riemann problem for quasilinear hyperbolic systems of conservation laws. Assuming that this problem has an entropy weak solution globally defined on t≥0 , we construct an asymptotic expansion of this solution, which is also globally defined in time. For technical reasons, we treat the case where the solution is only composed of shock waves or contact discontinuities. We expect that this expansion gives an approximation to the exact solution, which remains valid uniformly in time. Moreover, some improvements of our general results are obtained for the isentropic gas dynamics system.