Open Access
2015 A Weak Solution of a Stochastic Nonlinear Problem
M. L. Hadji
Abstr. Appl. Anal. 2015: 1-8 (2015). DOI: 10.1155/2015/482410


We consider a problem modeling a porous medium with a random perturbation. This model occurs in many applications such as biology, medical sciences, oil exploitation, and chemical engineering. Many authors focused their study mostly on the deterministic case. The more classical one was due to Biot in the 50s, where he suggested to ignore everything that happens at the microscopic level, to apply the principles of the continuum mechanics at the macroscopic level. Here we consider a stochastic problem, that is, a problem with a random perturbation. First we prove a result on the existence and uniqueness of the solution, by making use of the weak formulation. Furthermore, we use a numerical scheme based on finite differences to present numerical results.


Download Citation

M. L. Hadji. "A Weak Solution of a Stochastic Nonlinear Problem." Abstr. Appl. Anal. 2015 1 - 8, 2015.


Published: 2015
First available in Project Euclid: 15 April 2015

zbMATH: 07095578
MathSciNet: MR3312747
Digital Object Identifier: 10.1155/2015/482410

Rights: Copyright © 2015 Hindawi

Vol.2015 • 2015
Back to Top