Homogenization of trajectory attractors of Ginzburg-Landau equations with randomly oscillating terms

Abstract

We consider complex Ginzburg-Landau (GL) type equations of the form: \begin{document}${\partial _t}u = (1 + \alpha i)\Delta u + R{\mkern 1mu} u + (1 + \beta i)|u{|^2}u + g,$ \end{document} where $R$, $β$, and $g$ are random rapidly oscillating real functions. Assuming that the random functions are ergodic and statistically homogeneous in space variables, we prove that the trajectory attractors of these systems tend to the trajectory attractors of the homogenized equations whose terms are the average of the corresponding terms of the initial systems.Bibliography: 52 titles.