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., 2021, Volume 498,Pages <nobr>10

This article is cited in 3 papers

MATHEMATICS

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

K. A. Bekmaganbetov^ab, V. V. Chepyzhov^cd, G. A. Chechkin^bef

^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

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.

UDC: 517.957

Presented: V. V. Kozlov
Received: 18.02.2021
Revised: 18.02.2021
Accepted: 09.03.2021

DOI: 10.31857/S2686954321030036