ON ATTRACTORS OF GINZBURG–LANDAU EQUATIONS IN DOMAIN WITH LOCALLY PERIODIC MICROSTRUCTURE. SUBCRITICAL, CRITICAL AND SUPERCRITICAL CASES-Reference-Cited by-同舟云学术

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

Published:2023-09-01 Issue:1 Volume:513 Page:9-14
ISSN:2686-9543
Container-title:Доклады Российской академии наук. Математика, информатика, процессы управления
language:
Short-container-title:Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ

Author:

Bekmaganbetov К.А.¹²,Tolemys A. A.³²,Chepyzhov V. V.⁴,Chechkin G.А.⁵⁶²

Affiliation:

1. Lomonosov Moscow State University, Kazakhstan Branch

2. Institute of Mathematics and Mathematical Modeling

3. Eurasian National University named after L.N. Gumilyov

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

5. Lomonosov Moscow State University

6. Institute of Mathematics with a Computer Center – a division of the Ufa Federal Research Center of the Russian Academy of Sciences

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).

Publisher

The Russian Academy of Sciences

Reference15 articles.

1. Bekmaganbetov K.A., Chechkin G.A., Chepyzhov V.V. Strong Convergence of Trajectory Attractors for Reaction–Diffusion Systems with Random Rapidly Oscillating Terms // Communications on Pure and Applied Analysis (CPAA). 2020. V. 19. № 5. P. 2419–2443.

2. Bekmaganbetov K.A., Chechkin G.A., Chepyzhov V.V. “Strange Term” in Homogenization of Attractors of Reaction–Diffusion Equation in Perforated Domain // Chaos, Solitons & Fractals. 2020. V. 140. Art. No 110208.

3. Бекмаганбетов К.А., Толеубай А.М., Чечкин Г.А. Об аттракторах системы уравнений Навье–Стокса в двумерной пористой среде // Проблемы математического анализа. 2022. Т. 115. С. 15–28.

4. Chechkin G.A., Chepyzhov V.V., Pankratov L.S. Homogenization of Trajectory Attractors of Ginzburg–Landau equations with Randomly Oscillating Terms // Discrete and Continuous Dynamical Systems. Series B (DCDS-B). 2018. V. 23. № 3. P. 1133–1154.

5. Бекмаганбетов К.А., Чепыжов В.В., Чечкин Г.А. Сильная сходимость аттракторов системы реакции–диффузии с быстро осциллирующими членами в ортотропной пористой среде // Известия РАН. Серия математическая. 2022. Т. 86. № 6. С. 47–78.