Attractors of Ginzburg–Landau equations with oscillating terms in porous media: homogenization procedure
Bekmaganbetov K.A. Chechkin G.A. Tolemis A.A.
2024Taylor and Francis Ltd.
Applicable Analysis
2024#103Issue 129 - 44 pp.
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.
Attractors , Ginzburg–Landau equation , homogenization , perforated domain , weak convergence
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Department of Fundamental and Applied Mathematics, M.V. Lomonosov Moscow State University, Kazakhstan Branch, Astana, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Deparment of Differential Equations, Faculty of Mechanics and Mathematics, M.V. Lomonosov Moscow State University, Moscow, Russian Federation
Institute of Mathematics with Computing Center – Subdivision of the Ufa, Federal Research Center of Russian Academy of Science, Ufa, Russian Federation
Department of Fundamental Mathematics, L.N. Gumilev Eurasian National University, Astana, Kazakhstan
Department of Fundamental and Applied Mathematics
Institute of Mathematics and Mathematical Modeling
Deparment of Differential Equations
Institute of Mathematics with Computing Center – Subdivision of the Ufa
Department of Fundamental Mathematics
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