English

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

Probability 2023-01-02 v1

Abstract

In this paper, we consider a class of slow-fast systems of stochastic partial differential equations where the nonlinearity in the slow equation is not continuous and unbounded. We first provide conditions that ensure the existence of a martingale solution. Then we prove that the laws of the slow motions are tight, and any of their limiting points is a martingale solution for a suitable averaged equation. Our results apply to systems of stochastic reaction-diffusion equations where the reaction term in the slow equation is only continuous and has polynomial growth.

Keywords

Cite

@article{arxiv.2212.14552,
  title  = {Averaging principle for slow-fast systems of stochastic PDEs with rough coefficients},
  author = {Sandra Cerrai and Yichun Zhu},
  journal= {arXiv preprint arXiv:2212.14552},
  year   = {2023}
}