On Attractors of Ginzburg–Landau Equations in Domain with Locally Periodic Microstructure: Subcritical, Critical, and Supercritical Cases
Kuanysh Abdrakhmanovich Bekmaganbetov, A. A. Tolemys, Vladimir Victorovich Chepyzhov, Gregory Aleksandrovich Chechkin · Doklady Mathematics · 2023
Abstract In the paper we consider a problem for complex Ginzburg–Landau equations in a medium with locally periodic small obstacles. It is assumed that the obstacle surface can have different conductivity coefficients. We prove that the trajectory attractors of this system converge in a certain weak topology to the trajectory attractors of the homogenized Ginzburg–Landau equations with an additional potential (in the critical case), without an additional potential (in the subcritical case) in the medium without obstacles, or disappear (in the supercritical case).