Comptes Rendus
no. 11-12
Homogenization of random attractors for reaction–diffusion systems
Kuanysh A. Bekmaganbetov1; Gregory A. Chechkin2 ; Vladimir V. Chepyzhov3, 4
1 M.V. Lomonosov Moscow State University, Kazakhstan Branch, Kazhymukan st. 11, Astana, 010010, Kazakhstan
2 Department of Differential Equations, Faculty of Mechanics and Mathematics, M.V. Lomonosov Moscow State University, Moscow 119991, Russia
3 Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow 127994, Russia
4 National Research University Higher School of Economics, Moscow 101000, Russia
Comptes Rendus. Mécanique, Volume 344 (2016) no. 11-12, pp. 753-758.

We consider reaction–diffusion systems with randomly oscillating terms. We construct the deterministic homogenized reaction–diffusion system and prove that the trajectory attractors of the initial systems converge to the trajectory attractors of the homogenized systems.

Nous considérons les systèmes d'équations de réaction–diffusion avec termes aléatoirement oscillants. Nous construisons le système homogénéisé déterministe d'équations et prouvons que les attracteurs trajectoires des systèmes initiaux convergent vers les attracteurs trajectoires des systèmes d'équations homogénéisées.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2016.10.015
Keywords: Reaction–diffusion systems, Attractors, Homogenization, Random functions
Mots-clés : Systèmes de réaction–diffusion, Attracteurs, Homogénéisation, Fonctions aléatoires

Kuanysh A. Bekmaganbetov 1; Gregory A. Chechkin 2; Vladimir V. Chepyzhov 3, 4

1 M.V. Lomonosov Moscow State University, Kazakhstan Branch, Kazhymukan st. 11, Astana, 010010, Kazakhstan
2 Department of Differential Equations, Faculty of Mechanics and Mathematics, M.V. Lomonosov Moscow State University, Moscow 119991, Russia
3 Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow 127994, Russia
4 National Research University Higher School of Economics, Moscow 101000, Russia 
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Kuanysh A. Bekmaganbetov; Gregory A. Chechkin; Vladimir V. Chepyzhov. Homogenization of random attractors for reaction–diffusion systems. Comptes Rendus. Mécanique, Volume 344 (2016) no. 11-12, pp. 753-758. doi : 10.1016/j.crme.2016.10.015. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2016.10.015/

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Cited by Sources:

☆ GAC and VVC were partially supported by RFBR grants 15-01-07920 and 14-01-00346. KAB was partially supported by the Committee of Science of the Ministry of Education and Science of the Republic of Kazakhstan (CS MES RK) no. 0816/GF4.

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