Application of Fatou’s Lemma for Strong Homogenization of Attractors to Reaction–Diffusion Systems with Rapidly Oscillating Coefficients in Orthotropic Media with Periodic Obstacles

Kuanysh A. Bekmaganbetov, Gregory A. Chechkin () and Vladimir V. Chepyzhov
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Kuanysh A. Bekmaganbetov: Faculty of Mechanics and Mathematics, Kazakhstan Branch of M.V. Lomonosov Moscow State University, Astana 010010, Kazakhstan
Gregory A. Chechkin: Institute of Mathematics and Mathematical Modeling, Almaty 050010, Kazakhstan
Vladimir V. Chepyzhov: Institute for Information Transmission Problems, Russian Academy of Sciences, 127051 Moscow, Russia

Mathematics, 2023, vol. 11, issue 6, 1-21

Abstract: We study reaction–diffusion systems with rapidly oscillating terms in the coefficients of equations and in the boundary conditions, in media with periodic obstacles. The non-linear terms of the equations only satisfy general dissipation conditions. We construct trajectory attractors for such systems in the strong topology of the corresponding trajectory dynamical systems. By means of generalized Fatou’s lemma we prove the strong convergence of the trajectory attractors of considered systems to the trajectory attractors of the corresponding homogenized reaction–diffusion systems which contain an additional potential.

Keywords: trajectory attractors; homogenization; reaction–diffusion systems; non-linear equations; strong convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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