Global attractors for a Kirchhoff type plate equation with memory

Abstract

A Kirchho¤ type plate equation with memory is investigated. Under the suitable assumptions, we establish the existence of a global attractor by using the contraction function method.

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

“…As for deterministic plate equations, many authors have showed the existence of global attractors (see [1][2][3][4][5][6][7][8][9]). For the stochastic case, the existence of random attractors for plate equations has been investigated in [10,11,12] on bounded domains.…”

Asymptotic behavior for stochastic plate equations with rotational inertia and Kelvin-Voigt dissipative term on unbounded domains

“…The global attractors of the deterministic plate equation (i.e. h = 0) have been studied extensively in many literatures, see, e.g., [2,9,15,19,29,31,32,35,36,38] for the case of the bounded domain and [11,12,13,30,37] on unbounded domain. Yang [33] obtained the existence of the global attractors for the following elastic waveguide model in R n u tt − ∆u − ∆u tt + ∆ 2 u − ∆u t + u t + u − ∆g(x, u) = f (x), in R n × R + , u(x, 0) = u 0 (x), u t (x, 0) = u 1 (x), x ∈ R n .…”