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

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