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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2021, Volume 498, Pages 10–15
DOI: https://doi.org/10.31857/S2686954321030036 (Mi danma169) 		 
This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICS

On attractors of reaction–diffusion equations in a porous orthotropic medium

K. A. Bekmaganbetovab, V. V. Chepyzhovcd, G. A. Chechkinbef

a Lomonosov Moscow State University, Kazakhstan Branch, Nur-Sultan, Kazakhstan
b Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
c Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow, Russia
d National Research University "Higher School of Economics", Moscow, Russia
e Lomonosov Moscow State University, Moscow, Russia
f Institute of Mathematics with Computing Center, Ufa Federal Research Center, Russian Academy of Science, Ufa, Bashkortostan, Russia
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DOI: https://doi.org/10.31857/S2686954321030036
Abstract: A system of reaction–diffusion equations in a perforated domain with rapidly oscillating terms in the equation and in the boundary conditions is studied. A nonlinear function in the equations may not satisfy the Lipschitz condition and, hence, the uniqueness theorem for the corresponding initial–boundary value problem for the considered system of reaction–diffusion equations may not be satisfied. It is proved that the trajectory attractors of this system weakly converge in the corresponding topology to the trajectory attractors of the homogenized reaction–diffusion system with a “strange term” (potential).
Keywords: attractors, homogenization, reaction–diffusion equation, nonlinear equations, weak convergence, perforated domain, rapidly oscillating terms strange term.
Funding agency Grant number
Ministry of Education and Science of the Republic of Kazakhstan AR08855579
Russian Foundation for Basic Research 20-01-00469
Russian Science Foundation 20-11-20272
The first author’s research was supported by the Ministry of Education and Science of the Republic of Kazakhstan, grant no. AR08855579. The second author’s study (presented in Section 1) was supported by the Russian Foundation for Basic Research, project no. 20-01-00469. The third author’s work (in Section 2) was supported by the Russian Science Foundation, project no. 20-11-20272.
Presented: V. V. Kozlov
Received: 18.02.2021
Revised: 18.02.2021
Accepted: 09.03.2021
English version:
Doklady Mathematics, 2021, Volume 103, Issue 3, Pages 103–107
DOI: https://doi.org/10.1134/S1064562421030030
Bibliographic databases:
Document Type: Article
UDC: 517.957
Language: Russian
Citation: K. A. Bekmaganbetov, V. V. Chepyzhov, G. A. Chechkin, “On attractors of reaction–diffusion equations in a porous orthotropic medium”, Dokl. RAN. Math. Inf. Proc. Upr., 498 (2021), 10–15; Dokl. Math., 103:3 (2021), 103–107
Citation in format AMSBIB
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