Abstract
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. We finish our work by doing numerical simulations to validate our theoretical results.
Highlights
The mathematical modeling of the dynamics of granular materials is a fascinating subject as evidenced by the numerous studies which treat this subject in the literature
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
Summary
The mathematical modeling of the dynamics of granular materials is a fascinating subject as evidenced by the numerous studies which treat this subject in the literature. We have recently partially provided solutions to these questions where we study the Prigozhin model with Neumann and Robin boundaries conditions (see [10]) These types of conditions are interpreted by the presence of an obstacle for example a wall at the boundary and which prevents the sand escaping. Mance, since a nonlinear relation exists between the performance pressure tangential gradient and the fluid velocity along the well (see [11] [12] for details) Another application of this type of the boundary condition is in the study of the heat conduction within linear thermoelasticity (see [13] [14] [15]), and for the reaction-diffusion equation (see [16] [17]).
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