Averaging principle for slow–fast systems of stochastic PDEs with rough coefficients

Abstract

This paper examines a class of slow–fast systems of stochastic partial differential equations in which the nonlinearity in the slow equation is unbounded and discontinuous. We establish conditions that guarantee the existence of a martingale solution, and we demonstrate that the laws of the slow motions are tight, with any of their limiting points serving as a martingale solution for an appropriate averaged equation. Our findings have particular relevance for systems of stochastic reaction–diffusion equations, where the reaction term in the slow equation is only continuous and has arbitrary polynomial growth.