Comptes Rendus
Attractors and a “strange term” in homogenized equation
[Attracteurs et un « terme étrange » dans les équations homogénéisées]
Comptes Rendus. Mécanique, Volume 348 (2020) no. 5, pp. 351-359.

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 :
Accepté le :
Publié le :
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

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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     title = {Attractors and a {\textquotedblleft}strange term{\textquotedblright} in homogenized equation},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {351--359},
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     year = {2020},
     doi = {10.5802/crmeca.1},
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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/

[1] V. A. Marchenko; E. Ya. Khruslov Boundary Value Problems in Domains with Fine-Grain Boundary, Naukova Dumka, Kiev, 1974 (Russian) | Zbl

[2] V. A. Marchenko; E. Ya. Khruslov Homogenization of Partial Differential Equations, Birkhäuser, Boston (MA), 2006 | DOI | Zbl

[3] D. Cioranescu; F. Murat Un terme étrange venu d’ailleurs I & II, Nonlinear Partial Differential Equations and their Applications. Collège de France Seminar, Volume II & III (H. Berzis; J. L. Lions, eds.) (Research Notes in Mathematics), Volume 60 & 70, Pitman, London, 1982 (98-138 & 154-178) | Zbl

[4] A. G. Belyaev; A. L. Piatnitski; G. A. Chechkin Asymptotic behavior of a solution to a boundary value problem in a perforated domain with oscillating boundary, Sib. Math. J., Volume 39 (1998) no. 4, pp. 621-644 Translated from Sib. Mat. Z. 39 (1998) no. 4, p. 730-754) | DOI | Zbl

[5] G. A. Chechkin; A. L. Piatnitski Homogenization of boundary–value problem in a locally periodic perforated domain, Appl. Anal., Volume 71 (1999) no. 1-4, pp. 215-235 | DOI | MR | Zbl

[6] A. G. Belyaev; A. L. Piatnitski; G. A. Chechkin Averaging in a perforated domain with an oscillating third boundary condition, Russ. Acad. Sci. Sb. Math., Volume 192 (2001) no. 7, pp. 933-949 Translated from Mat. Sb. 192 (2001) no. 7, p. 3-20) | MR | Zbl

[7] V. V. Chepyzhov; M. I. Vishik Trajectory attractors for reaction–diffusion systems, Top. Meth. Nonlin. Anal. J. Julius Schauder Center, Volume 7 (1996) no. 1, pp. 49-76 | MR | Zbl

[8] V. V. Chepyzhov; M. I. Vishik Attractors for Equations of Mathematical Physics, American Mathematical Society, Providence (RI), 2002 | Zbl

[9] A. V. Babin; M. I. Vishik Attractors of Evolution Equations, North–Holland, Amsterdam, 1992 (Moscow: Nauka; 1989) | Zbl

[10] K. A. Bekmaganbetov; G. A. Chechkin; V. V. Chepyzhov Weak convergence of attractors of reaction–diffusion systems with randomly oscillating coefficients, Appl. Anal., Volume 98 (2019) no. 1-2, pp. 256-271 | DOI | MR | Zbl

[11] F. Boyer; P. Fabrie Mathematical tools for the study of the incompressible Navier–Stokes equations and related models, Applied Mathematical Sciences, Volume 183, Springer, New York (NY), 2013 | DOI | MR | Zbl

[12] V. V. Jikov; S. M. Kozlov; O. A. Oleinik Homogenization of Differential Operators and Integral Functionals, Springer Verlag, Berlin–New York, 1994

[13] É. Sanchez-Palencia Homogenization Techniques for Composite Media, Springer–Verlag, Berlin, 1987 | DOI | Zbl

[14] V. P. Mikhailov Partial Differential Equations, Mir, Moscow, 1978

[15] J. I. Diaz; D. Gomez-Castro; T. A. Shaposhnikova; M. N. Zubova Classification of homogenized limits of diffusion problems with spatially dependent reaction over critical-size particles, Appl. Anal., Volume 98 (2018) no. 1-2, pp. 232-255 | DOI | MR | Zbl

[16] R. Temam Infinite-dimensional Dynamical Systems in Mechanics and Physics, Applied Mathematics Series, 68, Springer-Verlag, New York (NY), 1988

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