Homogenization of attractors to reaction-diffusion system in a medium with random obstacles

Kuanysh A. Bekmaganbetov; Gregory A. Chechkin; Vladimir V. Chepyzhov

doi:10.3934/dcds.2024066

Article Contents

2024, Volume 44, Issue 11: 3474-3490. Doi: 10.3934/dcds.2024066

This issue Previous Article Uniqueness and nondegeneracy of ground states for the Schrödinger-Newton equation with power nonlinearity Next Article Stability of P-cyclic closed characteristics on P-symmetric compact convex hypersurfaces in $ \mathbb{R}^{2n} $

Homogenization of attractors to reaction-diffusion system in a medium with random obstacles

1.
M.V. Lomonosov Moscow State University, Kazakhstan Branch, Astana, Kazakhstan
2.
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
3.
M.V. Lomonosov Moscow State University, Moscow, Russia
4.
Institute of Mathematics with Computing Center, Subdivision of the Ufa Federal Research Center of Russian Academy of Science, Ufa, Russia
5.
Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia
6.
National Research University Higher School of Economics, Moscow, Russia

^* Corresponding author: G.A.Chechkin
^* Corresponding author: G.A.Chechkin

Received: March 2024

Revised: April 2024

Early access: May 2024

Published: November 2024

The work of the first author in Section 3 is partially supported by the Committee of Science of the Ministry of Science and Higher Education of the Republic of Kazakhstan (grant AP14869553). The work of the second author in Section 4 is supported in part by Russian Science Foundation (grant 20-11-20272) and in Section 5 by Ministry of Science and Higher Education of the Russian Federation as part of the program of the Moscow Center for Fundamental and Applied Mathematics. The work of the third author in Section 6 is partially supported by Russian Science Foundation (project 23-71-30008).

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Abstract

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.

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Mathematics Subject Classification: Primary: 35B40, 35B41, 35Q79.

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References

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