Affiliations: [a] Department of Mathematics, College of Science, Majmaah University, Zulfi 11932, Saudi Arabia | [b] African Institute for Mathematical Sciences (AIMS), Muizenberg, Cape Town, South Africa. E-mail: [email protected] | [c] Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Khartoum, Khartoum, Sudan. E-mail: [email protected]
Abstract: In this paper, we present homogenization and corrector results for stochastic linear parabolic equations in periodically perforated domains with non-homogeneous Robin conditions on the holes. We use the periodic unfolding method and probabilistic compactness results. Homogenization results presented in this paper are stochastic counterparts of some fundamental work given in [Cioranescu, Donato and Zaki in Port. Math. (N.S.) 63 (2006), 467–496]. We show that the sequence of solutions of the original problem converges in suitable topologies to the solution of a homogenized problem, which is a parabolic stochastic equation in fixed domain with Dirichlet condition on the boundary. In contrast to the two scale convergence method, the corrector results obtained in this paper are without any additional regularity assumptions on the solutions of the original problems.
