Pullback Attractor for Nonautonomous Ginzburg-Landau Equation with Additive Noise

Abstract

Long time behavior of stochastic Ginzburg-Landau equations with nonautonomous deterministic external forces, dispersion coefficients, and nonautonomous perturbations is studied. The domain is taken as a bounded interval $\mathcal{I}$ in $\mathbb{R}$. By making use of Sobolev embeddings and Gialiardo-Nirenberg inequality we obtain the existence and upper semicontinuity of the pullback attractor in $L^2(\mathcal{I})$ for the equation. The upper semicontinuity shows the stability of attractors under perturbations.