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).
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ACKNOWLEDGMENTS
The authors thank the anonymous peer reviewers for carefully reading the manuscript and providing comments that have helped significantly improve it.
Funding
The first and second authors’ research presented in Subsections 3.1 and 3.3 was supported by the Ministry of Science and Higher Education of the Republic of Kazakhstan, grant AP14869553. The fourth author’s research (Subsection 3.2) was supported by the Russian Science Foundation (project no. 20-11-20272) and (Section 2) by the Ministry of Science and Higher Education of the Russian Federation as part of the program of the Moscow Center for Fundamental and Applied Mathematics (agreement no. 075-15-2022-284).
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Translated by I. Ruzanova
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Bekmaganbetov, K.A., Tolemys, A.A., Chepyzhov, V.V. et al. On Attractors of Ginzburg–Landau Equations in Domain with Locally Periodic Microstructure: Subcritical, Critical, and Supercritical Cases. Dokl. Math. 108, 346–351 (2023). https://doi.org/10.1134/S1064562423701235
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DOI: https://doi.org/10.1134/S1064562423701235