Asymptotic behavior of stochastic fractional power dissipative equations on Rn. (November 2015)

• Record Type: Journal Article
• Authors: Lu, Hong; Bates, Peter W.; Xin, Jie; Zhang, Mingji
• Is Part Of: Nonlinear analysis. Volume 128(2015)
• Page Start: 176
• Page End: 198
• Publication Date: 2015-11
• Subjects: 37L55 -- 35B40 -- 35B41; Stochastic equation -- Fractional Laplacian -- Asymptotic compactness -- Random attractor -- Pullback attractor; 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.2015.06.033
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study a reaction–fractional diffusion equation with additive noise on the entire space R n with particular interest in the asymptotic behavior of solutions. We first transform the equation into a random equation whose solutions generate a random dynamical system. A priori estimates for solutions are derived when the nonlinearity satisfies certain growth conditions. Using estimates for far-field values of solutions and a cut-off technique, asymptotic compactness is proved. Thus, the existence of a random attractor in L 2 ( R n ) is established.