Attractors of the reaction-diffusion systems with rapidly oscillating coefficients and their homo\-genization.
type: Item
instance of: scholarly article
title: Attractors of the reaction-diffusion systems with rapidly oscillating coefficients and their homo\-genization.
zbMATH Open document ID: 1036.35038
DOI: 10.1016/S0294-1449(02)00115-4
author: S. V. Zelik
author: Messoud Efendiev
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 2002-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/78568
review text: The authors deal with the reaction-diffusion system in spatially non-homogeneous almost-periodic media. The vector valued function \(\vec u\) satisfies the differential system \(\partial_t {\vec u} = A_\varepsilon {\vec u} - f({\vec u}) + g\), \({\vec u}| _{\partial \Omega} = 0\). With natural assumptions on the nonlinear term \(f({\vec u})\), the long-time behavior of solutions \({\vec u}\) can be described in terms of the global attractor \({\mathcal A}^\varepsilon\) of the associated dynamical system and that the attractors \({\mathcal A}^\varepsilon\) converge to the attractor \({\mathcal A}^0\) of the homogenized problem as \(\varepsilon \rightarrow 0\). Moreover in the case of periodic media, explicit estimates are given for the distance between the non-homogenized \({\mathcal A}^\varepsilon\) and the homogenized \({\mathcal A}^0\) attractors in terms of the parameter \(\varepsilon\).
Mathematics Subject Classification ID: 35B41
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35B27
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35K50
Mathematics Subject Classification ID: 37L30
zbMATH DE Number: 1881304
zbMATH Keywords: almost-periodic media
zbMATH Keywords: long-time behavior
reviewed by: Marco Codegone
MaRDI profile type: Publication
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OpenAlex ID: W2059015209
description: scientific article; zbMATH DE number 1881304