Fractal dimension of random invariant sets for nonautonomous random dynamical systems and random attractor for stochastic damped wave equation. (March 2016)

• Record Type: Journal Article
• Authors: Zhou, Shengfan; Zhao, Min
• Is Part Of: Nonlinear analysis. Volume 133(2016)
• Page Start: 292
• Page End: 318
• Publication Date: 2016-03
• Subjects: 37L55 -- 35B41 -- 35B40; Stochastic damped wave equation -- Random attractor -- Random invariant set -- Fractal dimension -- Random dynamical system; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.12.013
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we first establish a criteria for estimating the upper bound of fractal dimension of a random compact invariant set of a non-autonomous random dynamical system on a separable Banach space and give some special conditions which can be easily verified to some stochastic partial differential equations for bounding the fractal dimension of random attractors. Then we apply these conditions to obtain an upper bound of fractal dimension of random attractor for stochastic damped wave equation with additive white noise.