Asymptotic behavior of stochastic complex Ginzburg-Landau equations with deterministic non-autonomous forcing on thin domains

Abstract

In this paper, we investigate the asymptotic behavior for nonautonomous stochastic complex Ginzburg-Landau equations with multiplicative noise on thin domains. For this aim, we first show that the existence and uniqueness of random attractors for the considered equations and the limit equations. Then, we establish the upper semicontinuity of these attractors when the thin domains collapse onto an interval.

Part-convergent cocycles and semi-convergent attractors of stochastic 2D-Ginzburg-Landau delay equations toward zero-memory

“…where A 0 (t, ω) ⊂ X is the PRA for the (non-delayed) stochastic 2D-GL equation (ρ = 0, F = 0, see [7,23,35,43]). Such robustness means that the delay attractors will not blow up at zero-memory.…”

“…So, we only obtain the part convergence of solutions for the initial data in Y . The convergence of solutions for all initial data in X remains open even for the non-delayed 2D-GL model (see [23]).…”

Regular random attractors for non-autonomous stochastic reaction-diffusion equations on thin domains

“…Random attractors have been investigated in [2,5,10,19,9] in the autonomous stochastic case, and in [3,21,22,23] in the non-autonomous stochastic case. Recently, the limiting dynamical behavior of stochastic partial differential equations on thin domain was studied in [16,20,13,14,11,12,17,4]. However, in [17,13], we only investigated the limiting behavior of random attractors in L 2 (O) of stochastic evolution equations on thin domain.…”