Homogenization for stochastic reaction-diffusion equations with singular perturbation term

Yangyang Shi; Hongjun Gao

doi:10.3934/dcdsb.2021137

Article Contents

2022, Volume 27, Issue 4: 2401-2426. Doi: 10.3934/dcdsb.2021137

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Homogenization for stochastic reaction-diffusion equations with singular perturbation term

Yangyang Shi^1, and
Hongjun Gao^2, ,

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
^* Corresponding author: gaohj@hotmail.com

Received: August 2020

Early access: May 2021

Published: April 2022

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

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Abstract

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.

Keywords:

Homogenization,
stochastic reaction-diffusion equations,
singular perturbations,
Kolmogorov equation.

Mathematics Subject Classification: Primary: 60H15, 70K70; Secondary: 37A25.

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