In this paper we study a dimensionless model of granular matter. The model can be rewritten into a system of balance laws. We prove that, every sufficiently small, compactly supported perturbation of a Lipschitz continuous decoupled initial data gives decoupled solution in finite time. Moreover, no gradient catastrophe occurs, i.e., the solution does not develop discontinuities. © 2007 Elsevier Inc. All rights reserved.
Shen, W. (2008). On the shape of avalanches. Journal of Mathematical Analysis and Applications, 339(2), 828–838. https://doi.org/10.1016/j.jmaa.2007.07.036