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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

  • 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.

    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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  • 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.


  • This article has been cited by:

    1. Graziano Crasta, Annalisa Malusa, Existence and uniqueness of solutions for a boundary value problem arising from granular matter theory, 2015, 259, 00220396, 3656, 10.1016/j.jde.2015.04.032
    2. Noureddine Igbida, A Partial Integrodifferential Equation in Granular Matter and Its Connection with a Stochastic Model, 2012, 44, 0036-1410, 1950, 10.1137/100810678
    3. A. Lo Giudice, G. Giammanco, D. Fransos, L. Preziosi, Modeling sand slides by a mechanics-based degenerate parabolic equation, 2019, 24, 1081-2865, 2558, 10.1177/1081286518755230
    4. Piermarco Cannarsa, Pierre Cardaliaguet, Carlo Sinestrari, On a Differential Model for Growing Sandpiles with Non-Regular Sources, 2009, 34, 0360-5302, 656, 10.1080/03605300902909966
    5. A. Adimurthi, Aekta Aggarwal, G.D. Veerappa Gowda, Godunov-type numerical methods for a model of granular flow, 2016, 305, 00219991, 1083, 10.1016/j.jcp.2015.09.036
    6. Aekta Aggarwal, G. D. Veerappa Gowda, Godunov-Type Numerical Methods for a Model of Granular Flow on Open Tables with Walls, 2016, 20, 1815-2406, 1071, 10.4208/cicp.290615.060516a
    7. Stefano Finzi Vita, 2010, Chapter 12, 978-88-470-1593-7, 157, 10.1007/978-88-470-1594-4_12
    8. Graziano Crasta, Ilaria Fragalà, A new symmetry criterion based on the distance function and applications to PDEʼs, 2013, 255, 00220396, 2082, 10.1016/j.jde.2013.06.003
    9. Roberto Nuca, Andrea Lo Giudice, Luigi Preziosi, Degenerate parabolic models for sand slides, 2021, 89, 0307904X, 1627, 10.1016/j.apm.2020.08.018
    10. A. Cattani, R.M. Colombo, G. Guerra, A hyperbolic model for granular flow, 2012, 92, 00442267, 72, 10.1002/zamm.201000181
    11. Noureddine Igbida, Fahd Karami, Thi Nguyet Nga Ta, Discrete collapsing sandpile model, 2014, 99, 0362546X, 177, 10.1016/j.na.2013.11.015
    12. Aekta Aggarwal, G.D. Veerappa Gowda, K. Sudarshan Kumar, A well-balanced second-order finite volume approximation for a coupled system of granular flow, 2024, 510, 00219991, 113068, 10.1016/j.jcp.2024.113068
    13. Piermarco Cannarsa, Stefano Finzi Vita, Sandpiles and Dunes: Mathematical Models for Granular Matter, 2024, 66, 0036-1445, 751, 10.1137/23M1583673
    14. Noureddine Igbida, José Miguel Urbano, A granular model for crowd motion and pedestrian flow, 2025, 111, 0024-6107, 10.1112/jlms.70184
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  • © 2008 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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