Asymptotic behavior of stochastic fractional power dissipative equations on R-n

作者：Lu, Hong; Bates, Peter W.^*; Xin, Jie; Zhang, Mingji

来源：Nonlinear Analysis-Theory Methods & Applications, 2015, 128: 176-198.

DOI：10.1016/j.na.2015.06.033

• Stochastic equation
• Fractional Laplacian
• Asymptotic compactness
• Random attractor
• Pullback attractor

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.

• 出版日期2015-11
• 单位中国矿业大学（北京）; 鲁东大学