Nonlinear Stability of Shock Fronts for a Relaxation System in Several Space Dimensions

We study the nonlinear asymptotic stability of planar shock front for a class of relaxation systems which approximate scalar conservation laws in several space dimensions time asymptotically. It is shown that if the relaxation system satisfies the subcharacteristic condition, then a traveling wave solution connecting a weak entropy shock is asymptotically stable under small generic perturbations.