Limiting behavior of invariant measures of stochastic reaction–diffusion equations on thin domains
Dingshi Li, Kening Lu, Bixiang Wang · Stochastics and Dynamics · 2024
This paper deals with the limiting behavior of invariant measures of stochastic reaction–diffusion equations on thin domains. We first show the existence of invariant measures of the stochastic equations in a bounded domain in [Formula: see text] which can be viewed as a perturbation of a bounded domain in [Formula: see text]. We then prove that the set of all invariant measures of the perturbed equations is tight and any limit of invariant measures of the perturbed systems must be an invariant measure of the limiting system when the [Formula: see text]-dimensional thin domains collapses onto an [Formula: see text]-dimensional domain.