Limiting Viscosity Approach for the Riemann Problem in Isentropic Gas Dynamics.

摘要

We consider the Riemann problem for the equations of isentropic gas dynamics in Eulerian coordinates. We construct solutions of this problem as limits of solutions of a 'viscosity' regularized problem that is rigged so as to preserve the invariance of the original problem under dilatations of the independent variables. The solutions thus constructed may contain vacuum regions. Using the same approach, we also construct solutions of the Riemann problem in case the data contain a vacuum state. (eg)