Homogenization of Neumann problem for hyperbolic stochastic partial differential equations in perforated domains

Article type: Research Article

Authors: Mohammed, Mogtaba^{a; b; *} | Sango, Mamadou^a

Affiliations: [a] Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa. E-mail: mamadou.sango@up.ac.za | [b] Department of Mathematics, Sudan University of Science and Technology, Khartoum 11111, Sudan. E-mail: mogtaba.mohammed@gmail.com

Correspondence: [*] Corresponding author. E-mail: mogtaba.mohammed@gmail.com.

Abstract: In this paper, we investigate a linear hyperbolic stochastic partial differential equation (SPDE) with rapidly oscillating ϵ-periodic coefficients in a domain with small holes (of size-ϵ) under Neumann conditions on the boundary of the holes and Dirichlet condition on the exterior boundary. When the number of these holes approach infinity, i.e. their sizes approach zero, the homogenized problem is a hyperbolic SPDE with constant coefficients in the domain without perforations. Moreover the convergence of the associated energy to that of the homogenized system is established.

Keywords: homogenization, hyperbolic SPDEs, Neumann problem, perforated domains, probabilistic compactness results

DOI: 10.3233/ASY-151355

Journal: Asymptotic Analysis, vol. 97, no. 3-4, pp. 301-327, 2016