In this paper, we study the limiting behavior of dynamics for stochastic reaction-diffusion equations driven by an additive noise and a deterministic non-autonomous forcing on an (n + 1)-dimensional thin region when it collapses into an n-dimensional region. We first established the existence of attractors and their properties for these equations on (n + 1)-dimensional thin domains. We then show that these attractors converge to the random attractor of the limit equation under the usual semi-distance as the thinness goes to zero.
A system of stochastic retarded reaction-diffusion equations with multiplicative noise and deterministic non-autonomous forcing on thin domains is considered. Relations between the asymptotic behavior for the stochastic retarded equations defined on thin domains in R n+1 and an equation on a domain in R n are investigated. We first show the existence and uniqueness of tempered random attractors for these equations. Then, we analyze convergence properties of the solutions as well as the attractors.
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