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

2023

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DOI 10.31857/s2686954323600180
Data confidence 70 medium
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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 on the obstacle surface one 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 the additional potential (in the subcritical case) in a medium without obstacles, or simply disappear (in the supercritical case).