Sigma-convergence of semilinear stochastic wave equations

Abstract: We address the homogenization of a semilinear hyperbolic stochastic partial differential equation with highly oscillating coefficients, in the context of ergodic algebras with mean value. To achieve our goal, we use a suitable variant of the sigma-convergence concept that takes into account both the random and deterministic behaviours of the phenomenon modelled by the underlying problem. We also provide an appropriate scheme for the approximation of the effective coefficients. To illustrate our approach, we work out some concrete problems such as the periodic homogenization problem, the almost periodic and the asymptotically almost periodic ones, and many more besides.