Global Attractors of the Extensible Plate Equations with Nonlinear Damping and Memory

Abstract

We prove in this paper the existence of a global attractor for the plate equations of Kirchhoff type with nonlinear damping and memory 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.…”

Random Attractor for Non-Autonomous Stochastic Extensible Plate Equation on Unbounded Domains

“…Barbosa and Ma [16] investigated the long-time behavior of an extensible plate equation with thermal memory. Yao and Ma [17] proved the existence of a global attractor for the plate equations of Kirchhoff type with nonlinear damping and memory using the contraction function method.…”

Attractor of the Kirchhoff type plate equation with memory and nonlinear damping on the whole time-dependent space

“…For instance, in ( [26]) Yang and Zhong considered the plate equation with nonlinear damping on bounded domain; Khanmamedov investigated existence of global attractors for the plate equation with a localized damping and critical exponent in an unbounded domain in [7,8]; the similar problem was studied by Xiao in [25]. While as µ = 0, the global attractor of Kirchhoff plate equation with memory was obtained in [23,28] and references therein.…”