Abstract
Abstract We study the asymptotic behavior of solutions to the non-autonomous stochastic plate equation driven by additive noise defined on unbounded domains. We first prove the uniform estimates of solutions, and then establish the existence and upper semicontinuity of random attractors.
Highlights
We study the asymptotic behavior of solutions to the non-autonomous stochastic plate equation driven by additive noise de ned on unbounded domains
We rst prove the uniform estimates of solutions, and establish the existence and upper semicontinuity of random attractors
The existence and uniqueness of the global attractor of the corresponding dynamical system was studied in [1,2,3,4,5,6,7,8,9,10]; besides, the uniform attractor of the dynamical system generated by the non-autonomous plate equation was established in [11]
Summary
Consider the following non-autonomous stochastic plate equation with additive noise de ned in the entire space Rn: utt + αut + ∆. The study of the long-time dynamics of plate equations has become an outstanding area in the eld of the in nite-dimensional dynamical system. The existence and uniqueness of the global attractor of the corresponding dynamical system was studied in [1,2,3,4,5,6,7,8,9,10]; besides, the uniform attractor of the dynamical system generated by the non-autonomous plate equation was established in [11]. For the stochastic plate equations, if the forcing term g(x, t) = g(x), the existence of a random attractor of (1.1)-(1.2) on bounded domain have been proved in [12,13,14].
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