# American Institute of Mathematical Sciences

## Homogenization for stochastic reaction-diffusion equations with singular perturbation term

 1 Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China 2 School of Mathematics, Southeast University, Nanjing 211189, China

* Corresponding author: gaohj@hotmail.com

Received  August 2020 Published  May 2021

Fund Project: The second author is supported by NSFC Grant No. 11531006 and Science Climbing Program of Southeast University

The main purpose of this paper is to study the homogenization problem of stochastic reaction-diffusion equations with singular perturbation term. The difficulty in studying such problems is how to get the uniform estimates of the equations under the influence of the singularity term. Firstly, we use the properties of the elliptic equation corresponding to the generator to eliminate the influence of singular terms and obtain the uniform estimates of the slow equation and thus, get the tightness. Finally, we prove that under appropriate assumptions, the slow equation converges to a homogenization equation in law.

Citation: Yangyang Shi, Hongjun Gao. Homogenization for stochastic reaction-diffusion equations with singular perturbation term. Discrete & Continuous Dynamical Systems - B, doi: 10.3934/dcdsb.2021137
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