Higher-order Stability of Attractors for Stochastic Reaction-Diffusion Equation
The stability of random attractors of the stochastic reaction-diffusion equation with additive white noise is studied.First,with a general assumption on the nonlinear term,the solutions of the stochastic differential equation converge to the solutions of the deterministic equation in the initial space L2(RN),and the upper semi-continuity of the random attractors is obtained.In particular,by using the nonlinear decomposition and the difference estimation,we technically obtain the convergence of solutions and the upper semi-continuity of random attractors in Lp(RN)(p＞2),where p is the growth index of the nonlinear function.
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