ON ATTRACTORS OF GINZBURG–LANDAU EQUATIONS IN DOMAIN WITH LOCALLY PERIODIC MICROSTRUCTURE. SUBCRITICAL, CRITICAL AND SUPERCRITICAL CASES

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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 on the obstacle surface one 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 the additional potential (in the subcritical case) in a medium without obstacles, or simply disappear (in the supercritical case).

About the authors

К.А. Bekmaganbetov

Lomonosov Moscow State University, Kazakhstan Branch; Institute of Mathematics and Mathematical Modeling

Author for correspondence.
Email: bekmaganbetov-ka@yandex.kz
Kazakhstan, Astana; Kazakhstan, Almaty

A. A. Tolemys

Eurasian National University named after L.N. Gumilyov; Institute of Mathematics and Mathematical Modeling

Author for correspondence.
Email: abylaikhan9407@gmail.com
Kazakhstan, Astana; Kazakhstan, Almaty

V. V. Chepyzhov

Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute)

Author for correspondence.
Email: chep@iitp.ru
Russia, Moscow

G.А. Chechkin

Lomonosov Moscow State University; Institute of Mathematics with a Computer Center – a division of the Ufa Federal Research Center
of the Russian Academy of Sciences; Institute of Mathematics and Mathematical Modeling

Author for correspondence.
Email: chechkin@mech.math.msu.su
Russian Federation, Moscow; Russian Federation, Ufa; Kazakhstan, Almaty

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