Random attractors for Ginzburg–Landau equations driven by difference noise of a Wiener-like process

Abstract

Abstract We consider a Wong–Zakai process, which is the difference of a Wiener-like process. We then prove that there are random attractors for non-autonomous Ginzburg–Landau equations driven by linear multiplicative noise in terms of Wong–Zakai process and Wiener-like process, respectively. Moreover, we establish the upper semi-continuity of random attractors as the size of difference noise tends to zero.

Keywords

• Random attractors
• Random dynamical systems
• Ginzburg–Landau Equations
• Upper semi-continuity
• Wong–Zakai difference
• Wiener-like process