On the shape of avalanches

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Abstract

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.

Original languageEnglish (US)
Pages (from-to)828-838
Number of pages11
JournalJournal of Mathematical Analysis and Applications
Volume339
Issue number2
DOIs
StatePublished - Mar 15 2008

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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