Front Tracing Approximations for Slow Erosion

In this paper we study an integro-differential equation that arises in modeling slow erosion of granular flow. We construct piecewise constant approximate solutions, using a front tracing technique. Convergence of the approximate solutions is established through proper a priori estimates, which in turn gives global existence of BV solutions. Furthermore, continuous dependence on initial data and on the erosion function is derived, achieving well-posedness of the solutions.