On a Dual Formulation for Growing Sandpile Problem with Mixed Boundary Conditions

A collapsing sandpile problem with nonlocal boundary condition

“…The study of granular materials is an interesting subject both for the mathematical difficulties which ensue from it ( [21,22,13])and for the practical applications: modeling of the movement of sand dunes [10], modeling of glacier avalanches, modeling of lakes and rivers [20]. In this work, we theoretically and numerically study the collapse of a sand heap due to successions of avalanches of various sizes.…”

“…In order to simplify the analysis, we reduce the study of the dual problem to a subspace of the H div (Ω) space as we suggested in the previous works (see [7,8,13,17]). And we will show how this approach allows to efficiently approximate the solution of the minimization problem .…”

Growing Sandpile Problem with Local and Non-Local Boundaries Conditions

“…The present work is organized as follows. In the next section, we use the nonlinear semi-group theory (see [21]) to get the existence and uniqueness of a variational solution of (1) and the convergence of the approximate Euler discretization in time solutions to problem (1). In Section 3, we show how to compute the solution of Euler implicit time discretization of (1) using duality argument and in the last section, some results of numerical results are given.…”

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In this paper, we study a class of Prigozhin equation for growing sandpile problem subject to local and a non-local boundary condition. The problem is a generalized model for a growing sandpile problem with Neumann boundary condition (see [1]). By the semi-group theory, we prove the existence and uniqueness of the solution for the model and thanks to a duality method we do the numerical analysis of the problem.

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