TITLE:
Growing Sandpile Problem with Local and Non-Local Boundaries Conditions
AUTHORS:
Urbain Traoré
KEYWORDS:
Sandpile, Collapsing, Avalanche, Nonlinear Semi-Group, Nonlocal Boundary Conditions, Euler Discretization in Time, Time Dependent Gradient Constraints
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.9 No.10,
October
8,
2021
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.