Asymptotic behavior for non-autonomous stochastic plate equation on unbounded domains

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.

Existence of a random attractor for non-autonomous stochastic plate equations with additive noise and nonlinear damping on $\mathbb{R}^{n}$

“…As far as the stochastic case driven by additive noise goes, when the deterministic forcing term g is independent of time, that is, g(x, t) ≡ g(x), the existence of a random pullback attractor on bounded domain has been obtained in [17,20,21]. Recently, on the unbounded domain, the authors investigated the existence and upper semi-continuity of random attractors for stochastic plate equation with rotational inertia and Kelvin-Voigt dissipative term as well as dependent-on-time terms (see [36] for details) and asymptotic behavior for non-autonomous stochastic plate equation on unbounded domains [35]. To the best of our knowledge, it has not been considered by any predecessors for the stochastic plate equation with additive noise and nonlinear damping on unbounded domain.…”

Asymptotic Behavior of the Kirchhoff Type Stochastic Plate Equation on Unbounded Domains

“…For the stochastic case, the existence of random attractors for plate equations has been investigated in [10,11,12] on bounded domains. In addition, there are results about the existence of random attractors and asymptotic compactness for plate equations on unbounded domains in [13][14][15][16][17][18].…”

“…When M(s) ≡ 0 in (1), we have investigated the existence of a random attractor for plate equations with additive noise and nonlinear damping defined on R n (see [14]). However, when equation ( 1) is Kirchhoff type, the problem is not yet considered by any predecessors.…”

Asymptotic behavior for stochastic plate equations with memory and additive noise on unbounded domains

“…For the stochastic plate equations, if µ = 0 and the forcing term g(x, t) = g(x), then the existence of a random attractor of (1.1)-(1.2) on bounded domain have been proved in [15,16,12,14]; if µ = 0, the existence of random attractors for plate equations with memory and additive white noise on bounded domain were considered in [19,20]. Recently, on the unbounded domain, the authors investigated the asymptotic behavior for stochastic plate equation with additive noise and multiplicative noise (see [33,32,30,31] for details). To the best of our knowledge, it is not considered by any predecessors for the stochastic plate equation with additive noise and memory on unbounded domain.…”