Uniqueness of steady 1-D shock solutions in a finite nozzle via vanishing viscosity aguments

Abstract

This paper studies the uniqueness of steady 1-D shock solutions in a finite flat nozzle via vanishing viscosity arguments. It is proved that, for both barotropic gases and non-isentropic gases, the steady viscous shock solutions converge under the L 1 norm. Hence only one shock solution of the inviscid Euler system could be the limit as the viscosity coefficient goes to 0, which shows the uniqueness of the steady 1-D shock solution in a finite flat nozzle. Moreover, the position of the shock front for the limit shock solution is also obtained.