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

Abstract

Based on the abstract theory of pullback attractors of non-autonomous non-compact dynamical systems by differential equations with both dependent-time deterministic and stochastic forcing terms, introduced by Wang in (J. Differ. Equ. 253:1544-1583, 2012), we investigate the existence of pullback attractors for the non-autonomous stochastic plate equations with additive noise and nonlinear damping on R n .

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].…”

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.…”