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A generalized collapsing sandpile model

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Abstract

In this paper, we introduce a new model for the collapsing sandpile and we prove existence and uniqueness of a solution for the corresponding initial value problem. Moreover, we prove the convergence of the time-stepping approximation of the solution. We use subgradient flows for variational problems with time dependent gradient constraints. These gradient constraints are interpreted as the critical angles of the sandpile. In particular, our model produces an evolution in time of avalanches in a drying of a sandpile, rather than instantaneous collapse.

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Authors and Affiliations

  1. LAMFA, UMR 6140, Université de Picardie Jules Verne, 80038, Amiens, France

    Noureddine Igbida

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  1. Noureddine Igbida
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Correspondence to Noureddine Igbida.

Additional information

This work has been supported by the French A.N.R. Grant JC05-41831 and by “FLUPARTI” project (funded by “Conseil Régional de Picardie”).

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Igbida, N. A generalized collapsing sandpile model. Arch. Math. 94, 193–200 (2010). https://doi.org/10.1007/s00013-009-0038-z

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  • DOI: https://doi.org/10.1007/s00013-009-0038-z

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