An existence result for the sandpile problem on flat tables with walls

Graziano Crasta; Stefano Finzi Vita

doi:10.3934/nhm.2008.3.815

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2008, Volume 3, Issue 4: 815-830. Doi: 10.3934/nhm.2008.3.815

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An existence result for the sandpile problem on flat tables with walls

Graziano Crasta^1, and
Stefano Finzi Vita^1,

1.
Dipartimento di Matematica "G. Castelnuovo", Università di Roma I, P.le A. Moro 2-00185 Roma

Received: December 31, 2007

Revised: June 30, 2008

Published: November 2008

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Abstract

We derive an existence result for solutions of a differential system which characterizes the equilibria of a particular model in granular matter theory, the so-called partially open table problem for growing sandpiles. Such result generalizes a recent theorem of [6] established for the totally open table problem. Here, due to the presence of walls at the boundary, the surface flow density at the equilibrium may result no more continuous nor bounded, and its explicit mathematical characterization is obtained by domain decomposition techniques. At the same time we show how these solutions can be numerically computed as stationary solutions of a dynamical two-layer model for growing sandpiles and we present the results of some simulations.

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Mathematics Subject Classification: Primary 35C15; Secondary 35Q99.

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