Stability of Viscous Shock Waves Associated with Non-Convex Modes

In this paper we prove the time asymptotic stability of viscous shock profiles under perturbations of non-vanishing mass, where the profile is associated with a non-convex mode (i.e. with a not necessarily monotone eigenvalue ). We thus extend the result of [SX] to the case of non-convex modes and the result of [F1] to the case of non-zero mass perturbations