Nonlinear Stability of Shock Profiles for Non-convex Model Equations with Degenerate Shock

Abstract

This paper is concerned with the stability of shock profiles for one-dimensional non-convex equations of viscous materials. The main purpose is to show that the shock profile solution is stable in an appropriate weighted norm space for the case of the degenerate shock, provided that the shock is weak and the initial disturbance is small and of integral zero. The proof is given by means of an elementary but technical weighted energy method to the integrated system of the original one. Moreover, the stability result can be applied to the equation of van der Waals fluid and viscoelascity.