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

Xiaobin Yao

doi:10.1186/s13661-020-01346-z

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 mathbb{R}^{n}.

Highlights

Plate equations have been studied for many years because of their worth in certain physical areas such as vibration and elasticity theories of solid mechanics
The purpose of this paper is to investigate the following non-autonomous stochastic plate equations with additive noise and nonlinear damping defined in the entire space Rn: utt + h(ut) +
In order to scrutinize the large-time behavior and characterization of solution for the stochastic partial differential equations driven by noise, Crauel and Flandoi [7, 8], Flandoi and Schmalfuss [10], and Schmalfuss [19] introduced the concept of pullback attractors and established some abstract results for the existence of such attractors about compact dynamical system [1, 8, 10, 14, 15]

Summary

Introduction

Plate equations have been studied for many years because of their worth in certain physical areas such as vibration and elasticity theories of solid mechanics. Wang in [25] further extended the concept of asymptotic compactness to the case of partial differential equations with both random and time-dependent forcing terms; he applied these criteria into the stochastic reaction-diffusion equation with additive noise on Rn and obtained the existence of a unique pullback attractor.

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Conclusion