Open AccessHomogenization for stochastic reaction-diffusion equations with singular perturbation term
Author(s) -
Yangyang Shi,
Hongjun Gao
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021137
Subject(s) - homogenization (climate) , singular perturbation , singularity , mathematics , perturbation (astronomy) , mathematical analysis , term (time) , physics , biodiversity , ecology , quantum mechanics , biology
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.