Homogenization of Attractors of Reaction–Diffusion System with Rapidly Oscillating Terms in an Orthotropic Porous Medium

Bekmaganbetov K.A. Chepyzhov V.V. Chechkin G.A.
November 2021 Springer

Journal of Mathematical Sciences (United States)
2021 #259 Issue 2 148 - 166 pp.

In a perforated domain, we consider a reaction-diffusion system with rapidly oscillating terms in the equations and boundary conditions. No Lipschitz condition is imposed, so the uniqueness of a solution to the corresponding initial-boundary value problem is not guaranteed. We prove that the trajectory attractors of the system weakly converge to the trajectory attractors of the homogenized reaction-diffusion systems with a strange term (potential).

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Kazakhstan Branch of Lomonosov Moscow State University, 11, Kazhymukan St, Nur-Sultan, 010010, Kazakhstan
Institute of Mathematics and Mathematic Modeling MES RK, 125, Pushkina St, Almaty, 050010, Kazakhstan
Institute for Information Transmission Problems RAS, 19, Bol’shoi Karetnyi per, Moscow, 127051, Russian Federation
National Research University “Higher School of Economics”, 20, Myasnitskaya St, Moscow, 101978, Russian Federation
Lomonosov Moscow State University, Moscow, 119991, Russian Federation
Institute of Mathematics with Computing Center, 112, Chernyshevskogo St, Ufa, 450008, Russian Federation

Kazakhstan Branch of Lomonosov Moscow State University
Institute of Mathematics and Mathematic Modeling MES RK
Institute for Information Transmission Problems RAS
National Research University “Higher School of Economics”
Lomonosov Moscow State University
Institute of Mathematics with Computing Center

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