Homogenization of Attractors of Reaction–Diffusion System with Rapidly Oscillating Terms in an Orthotropic Porous Medium

In a perforated domain, we consider a reaction-diffusion system with rapidly oscillating terms in the equations and boundary conditions. No Lipschitz condition is imposed, so the uniqueness of a solution to the corresponding initial-boundary value problem is not guaranteed. We prove that the traject...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2021-11, Vol.259 (2), p.148-166
Main Authors: Bekmaganbetov, K. A., Chepyzhov, V. V., Chechkin, G. A.
Format: Article
Language:English
Subjects:
Boundary conditions
Boundary value problems
Differential equations
Diffusion
Lipschitz condition
Mathematics
Mathematics and Statistics
Porous media
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Summary:In a perforated domain, we consider a reaction-diffusion system with rapidly oscillating terms in the equations and boundary conditions. No Lipschitz condition is imposed, so the uniqueness of a solution to the corresponding initial-boundary value problem is not guaranteed. We prove that the trajectory attractors of the system weakly converge to the trajectory attractors of the homogenized reaction-diffusion systems with a strange term (potential).
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-021-05607-9