Homogenization of Neumann problem for hyperbolic stochastic partial differential equations in perforated domains
Mogtaba A. Y. Mohammed, Mamadou Sango · Asymptotic Analysis · 2016
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 th e 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.