Attractors and a “strange term” in homogenized equation

Kuanysh A. Bekmaganbetov; Gregory A. Chechkin; Vladimir V. Chepyzhov

doi:10.5802/crmeca.1

Attractors and a “strange term” in homogenized equation
[Attracteurs et un « terme étrange » dans les équations homogénéisées]

Kuanysh A. Bekmaganbetov ^1,² ; Gregory A. Chechkin ^3,⁴ ; Vladimir V. Chepyzhov ^5,⁶

¹ Institute of Mathematics and Mathematical Modeling, Pushkin st. 125, Almaty, 050010, Kazakhstan
² M. V. Lomonosov Moscow State University, Kazakhstan Branch, Kazhymukan st. 11, Nur-Sultan, 010010, Kazakhstan
³ Institute of Mathematics with Computing Center - Subdivision of the Ufa Federal Research Center of Russian Academy of Sciences, Chernyshevskogo st., 112, Ufa, 450008, Russia
⁴ M. V. Lomonosov Moscow State University, Leninskie Gory, 1, Moscow, 119991, Russia
⁵ Institute for Information Transmission Problems, Russian Academy of Sciences, Bolshoy Karetniy 19, Moscow 127994, Russia
⁶ National Research University Higher School of Economics, Moscow 101000, Russia

Comptes Rendus. Mécanique, Volume 348 (2020) no. 5, pp. 351-359.

Résumé
Abstract

Nous étudions le comportement des attracteurs de l’équation de réaction–diffusion dans le domaine perforé car le petit paramètre caractérisant la perforation tend vers zéro.

We study the behavior of attractors of the reaction–diffusion equation in a perforated domain as the small parameter characterizing the perforation tends to zero.

Reçu le : 2020-02-03
Accepté le : 2020-02-03
Publié le : 2020-11-10

DOI : 10.5802/crmeca.1

Classification : 35B30, 35B40, 35B45, 35B60, 35Q35, 76A05, 76D10
Keywords: Homogenization, Attractors, Reaction–diffusion equation, Boundary value problem, Perforated domain
Mot clés : Homogénéisation, Attracteurs, Équation de réaction–diffusion, Problème de valeur limite, Domaine perforé

Affiliations des auteurs :

Kuanysh A. Bekmaganbetov ^{1, 2} ; Gregory A. Chechkin ^{3, 4} ; Vladimir V. Chepyzhov ^{5, 6}

¹ Institute of Mathematics and Mathematical Modeling, Pushkin st. 125, Almaty, 050010, Kazakhstan
² M. V. Lomonosov Moscow State University, Kazakhstan Branch, Kazhymukan st. 11, Nur-Sultan, 010010, Kazakhstan
³ Institute of Mathematics with Computing Center - Subdivision of the Ufa Federal Research Center of Russian Academy of Sciences, Chernyshevskogo st., 112, Ufa, 450008, Russia
⁴ M. V. Lomonosov Moscow State University, Leninskie Gory, 1, Moscow, 119991, Russia
⁵ Institute for Information Transmission Problems, Russian Academy of Sciences, Bolshoy Karetniy 19, Moscow 127994, Russia
⁶ National Research University Higher School of Economics, Moscow 101000, Russia

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Kuanysh A. Bekmaganbetov and Gregory A. Chechkin and Vladimir V. Chepyzhov},
     title = {Attractors and a {\textquotedblleft}strange term{\textquotedblright} in homogenized equation},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {351--359},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {348},
     number = {5},
     year = {2020},
     doi = {10.5802/crmeca.1},
     language = {en},
}

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Kuanysh A. Bekmaganbetov; Gregory A. Chechkin; Vladimir V. Chepyzhov. Attractors and a “strange term” in homogenized equation. Comptes Rendus. Mécanique, Volume 348 (2020) no. 5, pp. 351-359. doi : 10.5802/crmeca.1. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.1/

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