Effective dynamics for a class of stochastic weakly damped wave equation with a fast oscillation

Abstract

The purpose of this paper is to consider the effective dynamic behavior of a class of stochastic weakly damped wave equations with a fast oscillation under the non-Lipschitz condition. We show that the slow component converges to the solution of the corresponding average equation. The result presented here extends the existing results from the Lipschitz to non-Lipschitz condition, which is a much weaker condition with a wider range of applications.