Approximate dynamics of stochastic partial differential equations under fast dynamical boundary conditions

Abstract

This work is concerned with a class of stochastic partial differential equations with a fast random dynamical boundary condition. In the limit of fast diffusion, it derives an effective stochastic partial differential equation to describe the evolution of the dominant pattern. Using the multiscale analysis and the averaging principle, it then establishes deviation estimates of the original stochastic system towards the effective approximating system. A concrete example further illustrates the result on a large time scale.