HOMOGENIZATION OF ATTRACTORS TO REACTION-DIFFUSION SYSTEM IN A MEDIUM WITH RANDOM OBSTACLES
Bekmaganbetov K.A. Chechkin G.A. Chepyzhov V.V.
November 2024American Institute of Mathematical Sciences
Discrete and Continuous Dynamical Systems- Series A
2024#44Issue 113474 - 3490 pp.
A reaction-diffusion system in a domain with randomly located obstacles was considered. When studying the problem, we sat the homogeneous Dirichlet condition on the outer boundary of the domain and the Neumann condition on the boundary of the cavities. Under such assumptions, it was proven that random trajectory attractors of this system with random coefficients converge in some weak topology to the deterministic trajectory attractor of a homogenized reaction-diffusion system with deterministic coefficients in a homogeneous domain without obstacles. In the case of uniqueness, we obtained weak convergence of random global attractors to a deterministic global attractor. Bibliography: 19 titles.
Attractors , compactness , homogenization , nonlinear equations , random porous medium , randomly perforated domains , reaction-diffusion system , topological space , weak convergence
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M.V. Lomonosov Moscow State University, Kazakhstan Branch, Astana, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
M.V. Lomonosov Moscow State University, Moscow, Russian Federation
Institute of Mathematics with Computing Center, Subdivision of the Ufa Federal Research Center, Russian Academy of Science, Ufa, Russian Federation
Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russian Federation
National Research University Higher School of Economics, Moscow, Russian Federation
M.V. Lomonosov Moscow State University
Institute of Mathematics and Mathematical Modeling
M.V. Lomonosov Moscow State University
Institute of Mathematics with Computing Center
Institute for Information Transmission Problems
National Research University Higher School of Economics
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