On Dynamical Behavior Of Stochastic Viscous Cahn-Hilliard Equation

This paper is devoted to the study of attractor of stochastic viscous Cahn-Hilliardequation driven by white noise, d（（1-α）u-α△u）+（△²u-△f（u））dt=dW,（x, t）∈G×（t₀,∞）,（2） u（x, t）=0,（x, t）∈G×[t₀,∞),on a bounded domain, where α, μ∈[0,1] are parameters. For any given μ∈(0,1], underreasonable assumptions, we first show that the problem has a stochastic global attractorAα,μ（ω） H²（G）∩H₀¹（G）, which pullback attracts every bounded deterministic setB H²（G）∩H₀¹（G） and then prove that Aα,μ（ω） is supper semicontinuous in α. Finally,we study, for fixed α∈[0,1], the continuity of Aα,μ（ω） and its Morse decompositionswith μ, and obtain（i） Aα,μ（ω） and its Morse decompositions are supper semicontinuous in μ at μ=0.（ii） Aα,μ（ω） is lower semicontinuous in μ at μ=0.