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Giroire, J., Ha-Duong, T. and Moumas, V. (2005) A Non-Linear and Non-Local Boundary Condition for a Diffusion Equation in Petroleum Engineering. Mathematical Methods in the Applied Sciences, 28, 1527-1552.
https://doi.org/10.1002/mma.622

has been cited by the following article:

• 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.