Erosion profile by a global model for granular flow
Wen Shen and Tianyou Zhang
Abstract: In this paper we study an integro-differential equation that models the erosion of a mountain profile caused by small avalanches. The equation is in conservative form, with a non-local flux involving an integral of the moun tain slope. Under suitable assumptions on the erosion rate, the mountain profile develops several types of singularities, which we call kinks, shocks and hyper-kinks. We study formation of these singularities, and derive admissibility conditions. Furthermore, entropy weak solutions to the Cauchy problem are constructed globally in time, taking limits of piecewise affine approximate solutions. Entropy and entropy flux functions are introduced, and Lax entropy condition is established for the weak solutions.