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Preprint 2010-017

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.

Paper:
Available as PDF (426 Kbytes).
Author(s):
Wen Shen,
Tianyou Zhang,
Publishing information:
To appear in Archive for Rational Mechanics and Analysis
Comments:
Updated 2010-10-28, 2011-01-11 and 2012-02-07.
Submitted by:
; 2010-10-15.