Homogenization of nonlinear hyperbolic stochastic equation via Tartar’s method
Mogtaba A. Y. Mohammed · Journal of Hyperbolic Differential Equations · 2017
In this paper, We establish new homogenization results for stochastic nonlinear hyperbolic equations with periodically oscillating coefficients. We use a delicate blending of Tartar’s method of oscillating test functions and deep probabilistic compactness results due to Prokhorov and Skorokhod. We prove that the sequence of solutions of the original problem converges in suitable topologies to the solution of a homogenized stochastic hyperbolic problem with constant coefficients. We also prove the convergence of the associated energies.