On Attractors of Ginzburg–Landau Equations in Domain with Locally Periodic Microstructure: Subcritical, Critical, and Supercritical Cases

Bekmaganbetov K.A. Tolemys A.A. Chepyzhov V.V. Chechkin G.A.
October 2023 Pleiades Publishing

Doklady Mathematics
2023 #108 Issue 2 346 - 351 pp.

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).

attractors , Ginzburg–Landau equations , homogenization , nonlinear equations , perforated domain , rapidly oscillating terms , weak convergence

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Lomonosov Moscow State University, Kazakhstan Branch, Astana, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Gumilyov Eurasian National University, Astana, Kazakhstan
Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow, Russian Federation
Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russian Federation
Institute of Mathematics with Computer Center, Division of the Ufa Federal Research Center of the Russian Academy of Sciences, Ufa, Russian Federation

Lomonosov Moscow State University
Institute of Mathematics and Mathematical Modeling
Gumilyov Eurasian National University
Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute)
Faculty of Mechanics and Mathematics
Institute of Mathematics with Computer Center

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