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Applicable Analysis
An International Journal
Volume 103, 2024 - Issue 1
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Research Article

Attractors of Ginzburg–Landau equations with oscillating terms in porous media: homogenization procedure

Kuanysh A. Bekmaganbetova Department of Fundamental and Applied Mathematics, M.V. Lomonosov Moscow State University, Kazakhstan Branch, Astana, Kazakhstan;b Institute of Mathematics and Mathematical Modeling, Almaty, KazakhstanORCID Iconhttps://orcid.org/0000-0001-6259-4383View further author information
ORCID Icon,
Gregory A. Chechkinb Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan;c Deparment of Differential Equations, Faculty of Mechanics and Mathematics, M.V. Lomonosov Moscow State University, Moscow, Russia;d Institute of Mathematics with Computing Center – Subdivision of the Ufa, Federal Research Center of Russian Academy of Science, Ufa, RussiaCorrespondence[email protected]
ORCID Iconhttps://orcid.org/0000-0002-7654-5803View further author information
ORCID Icon &
Abylaikhan A. Tolemise Department of Fundamental Mathematics, L.N. Gumilev Eurasian National University, Astana, KazakhstanORCID Iconhttps://orcid.org/0000-0003-4333-8258View further author information
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Pages 29-44 | Received 25 Nov 2021, Accepted 06 Oct 2022, Published online: 02 Feb 2023
 
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Abstract

We consider the Ginzburg–Landau equation in the perforated domain, with rapidly oscillating coefficients. We derive the homogenized Ginzburg–Landau equation with a ‘strange term’ (potential) and prove that the trajectory attractors of the given equation tend in a weak sense to the trajectory attractors of the homogenized one. Assuming additional conditions to be satisfied for the coefficients, we provide also a convergence of the global attractor.

AMS 2010 Mathematics Subject Classifications:

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The results of KAB and AAT in Sections 2 and 3 is supported in part by the Committee of Science of the Ministry of Science and Higher Education of the Republic of Kazakhstan (project AP14869553). The results of GAC in Section 4 is partially supported by Russian Science Foundation (project 20-11-20272).

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