Effective dynamics of stochastic wave equation with a random dynamical boundary condition

TL;DR

This paper derives an effective macroscopic stochastic wave equation from a complex model with random boundary conditions and perforations, simplifying the analysis of wave dynamics in heterogeneous media.

Contribution

It introduces a novel homogenization approach for stochastic wave equations with dynamical boundary conditions on perforated domains.

Findings

Derived a homogenized stochastic wave equation without small holes

Established the effective dynamics in the sense of probability distribution

Provided a new framework for analyzing stochastic wave equations with complex boundaries

Abstract

This work is devoted to the effective macroscopic dynamics of a weakly damped stochastic nonlinear wave equation with a random dynamical boundary condition. The white noises are taken into account not only in the model equation defined on a domain perforated with small holes, but also in the dynamical boundary condition on the boundaries of the small holes. An effective homogenized, macroscopic model is derived in the sense of probability distribution, which is a new stochastic wave equation on a unified domain, without small holes, with a usual static boundary condition.