Front tracking approximations for slow erosion

In this paper we study an integro-differential equation describing slow erosion, in a model of granular ow. In this equation the ux is non local and depends on x, t. We define approximate solutions by using a front tracking technique, adapted to this special equation. Convergence of the approximate solutions is established by means of suitable a priori estimates. In turn, these yield the global existence of entropy solutions in BV. Such entropy solutions are shown to be unique. We also prove the continuous dependence on initial data and on the erosion function, for the approximate as well as for the exact solutions. This establishes the well-posedness of the Cauchy problem.