Application of Fatou’s Lemma for Strong Homogenization of Attractors to Reaction–Diffusion Systems with Rapidly Oscillating Coefficients in Orthotropic Media with Periodic Obstacles
Bekmaganbetov K.A. Chechkin G.A. Chepyzhov V.V.
March 2023MDPI
Mathematics
2023#11Issue 6
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.
homogenization , non-linear equations , reaction–diffusion systems , strong convergence , trajectory attractors
Text of the article Перейти на текст статьи
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
Department of Differential Equations, Faculty of Mechanics and Mathematics, M.V. Lomonosov Moscow State University, Moscow, 119991, Russian Federation
Institute of Mathematics with Computing Center, Subdivision of the Ufa Federal Research Center of Russian Academy of Science, Ufa, 450008, Russian Federation
Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, 127051, Russian Federation
Faculty of Mechanics and Mathematics
Institute of Mathematics and Mathematical Modeling
Department of Differential Equations
Institute of Mathematics with Computing Center
Institute for Information Transmission Problems
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026