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

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  • Kuanysh A. Bekmaganbetov

    (Faculty of Mechanics and Mathematics, Kazakhstan Branch of M.V. Lomonosov Moscow State University, Astana 010010, Kazakhstan
    Institute of Mathematics and Mathematical Modeling, Almaty 050010, Kazakhstan
    These authors contributed equally to this work.)

  • Gregory A. Chechkin

    (Institute of Mathematics and Mathematical Modeling, Almaty 050010, Kazakhstan
    Department of Differential Equations, Faculty of Mechanics and Mathematics, M.V. Lomonosov Moscow State University, 119991 Moscow, Russia
    Institute of Mathematics with Computing Center, Subdivision of the Ufa Federal Research Center of Russian Academy of Science, 450008 Ufa, Russia
    These authors contributed equally to this work.)

  • Vladimir V. Chepyzhov

    (Institute for Information Transmission Problems, Russian Academy of Sciences, 127051 Moscow, Russia
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Kuanysh A. Bekmaganbetov & Gregory A. Chechkin & Vladimir V. Chepyzhov, 2023. "Application of Fatou’s Lemma for Strong Homogenization of Attractors to Reaction–Diffusion Systems with Rapidly Oscillating Coefficients in Orthotropic Media with Periodic Obstacles," Mathematics, MDPI, vol. 11(6), pages 1-21, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1448-:d:1099429
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    References listed on IDEAS

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    1. Gregory A. Chechkin, 2021. "The Meyers Estimates for Domains Perforated along the Boundary," Mathematics, MDPI, vol. 9(23), pages 1-11, November.
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