Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
839463 | Nonlinear Analysis: Theory, Methods & Applications | 2015 | 23 Pages |
Abstract
We study a reaction–fractional diffusion equation with additive noise on the entire space RnRn 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 L2(Rn)L2(Rn) is established.
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Authors
Hong Lu, Peter W. Bates, Jie Xin, Mingji Zhang,