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

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...

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Bibliographic Details
Published in:Doklady. Mathematics 2023-10, Vol.108 (2), p.346-351
Main Authors: Bekmaganbetov, K. A., Tolemys, A. A., Chepyzhov, V. V., Chechkin, G. A.
Format: Article
Language:English
Subjects:
Barriers
Landau-Ginzburg equations
Mathematical analysis
Mathematics
Mathematics and Statistics
Topology
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Summary: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).
ISSN:1064-5624
1531-8362
DOI:10.1134/S1064562423701235