Affiliations: [a] Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa. E-mail: [email protected] | [b] Department of Mathematics, College of Science, Majmaah University, Zulfi 11932, Saudi Arabia. E-mail: [email protected]
Abstract: In this paper, we present new homogenization results of a stochastic model for flow of a single-phase fluid through a partially fissured porous medium. The model is a double-porosity model with two flow fields, one associated with the system of fissures and the other associated with the porous system. This model is mathematically described by a system of nonlinear stochastic partial differential equations defined on perforated domain. The main tools to derive the homogenized stochastic model are the Nguetseng’s two-scale convergence, tightness of constructed probability measures, Prokhorov and Skorokhod compactness process and Minty’s monotonicity method.
