Article ID Journal Published Year Pages File Type
839463 Nonlinear Analysis: Theory, Methods & Applications 2015 23 Pages PDF
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.

Related Topics
Physical Sciences and Engineering Engineering Engineering (General)
Authors
, , , ,