Limiting dynamics for non-autonomous stochastic retarded reaction-diffusion equations on thin domains

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 Rⁿ⁺¹ and an equation on a domain in Rⁿ 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.