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

Graziano Crasta; Stefano Finzi Vita; Graziano Crasta; Stefano Finzi Vita

doi:10.3934/nhm.2008.3.815

Networks and Heterogeneous Media

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
,},
Stefano Finzi Vita ^{1
,}

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

Received: 01 January 2008 Revised: 01 July 2008
Primary 35C15; Secondary 35Q99

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.
- Distance function,
- granular matter,
- flat tray problem,
- Hamilton-Jacobi equations,
- mass transport
Citation: Graziano Crasta, Stefano Finzi Vita. An existence result for the sandpile problem on flat tables with walls[J]. Networks and Heterogeneous Media, 2008, 3(4): 815-830. doi: 10.3934/nhm.2008.3.815

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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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