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On Attractors of Reaction–Diffusion Equations in a Porous Orthotropic Medium


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).

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The first author’s research was supported by the Ministry of Education and Science of the Republic of Kazakhstan, grant no. AR08855579. The second author’s study (presented in Section 1) was supported by the Russian Foundation for Basic Research, project no. 20-01-00469. The third author’s work (in Section 2) was supported by the Russian Science Foundation, project no. 20-11-20272.

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Correspondence to K. A. Bekmaganbetov, V. V. Chepyzhov or G. A. Chechkin.

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Translated by I. Ruzanova

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Bekmaganbetov, K.A., Chepyzhov, V.V. & Chechkin, G.A. On Attractors of Reaction–Diffusion Equations in a Porous Orthotropic Medium. Dokl. Math. 103, 103–107 (2021).

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  • attractors
  • homogenization
  • reaction–diffusion equation
  • nonlinear equations
  • weak convergence
  • perforated domain
  • rapidly oscillating terms
  • strange term