Separation of solutions of quasilinear hyperbolic systems in the neighborhood of a large discontinuity

Abstract

We consider solutions of quasilinear hyperbolic systems of any dimension in one space variable. Locally, our solutions are differentiable excapt for a single jump discontinuity, either an entropy shock or a contacr discontinuity, which may be of any strengrth. With some additional assumptions. we show that the map of the initrial into the solutions at some later time is continuous in L1