On Attractors of Reaction–Diffusion Equations in a Porous Orthotropic Medium
Bekmaganbetov K.A. Chepyzhov V.V. Chechkin G.A.
May 2021Pleiades journals
Doklady Mathematics
2021#103Issue 3103 - 107 pp.
Abstract: A system of reaction–diffusion equations in a perforated domain with rapidly oscillating terms in the equation and in the boundary conditions is studied. A nonlinear function in the equations may not satisfy the Lipschitz condition and, hence, the uniqueness theorem for the corresponding initial–boundary value problem for the considered system of reaction–diffusion equations may not be satisfied. It is proved that the trajectory attractors of this system weakly converge in the corresponding topology to the trajectory attractors of the homogenized reaction–diffusion system with a “strange term” (potential).
attractors , homogenization , nonlinear equations , perforated domain , rapidly oscillating terms , reaction–diffusion equation , strange term , weak convergence
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Lomonosov Moscow State University, Kazakhstan Branch, Nur-Sultan, 010010, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Almaty, 050010, Kazakhstan
Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow, 127051, Russian Federation
National Research University Higher School of Economics, Moscow, 101000, Russian Federation
Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, 119991, Russian Federation
Institute of Mathematics with Computing Center, Ufa Federal Research Center, Russian Academy of Science, Ufa, 450000, Bashkortostan, Russian Federation
Lomonosov Moscow State University
Institute of Mathematics and Mathematical Modeling
Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute)
National Research University Higher School of Economics
Faculty of Mechanics and Mathematics
Institute of Mathematics with Computing Center
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