Uniform attractor for the partly dissipative nonautonomous lattice systems
type: Item
instance of: scholarly article
title: Uniform attractor for the partly dissipative nonautonomous lattice systems
zbMATH Open document ID: 1185.37163
DOI: 10.1155/2009/916316
author: Haishen Lv
author: Xiaojun Li
published in: Advances in Difference Equations
publication date: 2009-11-11T00:00:00Z
full work available at URL: https://eudml.org/doc/45783
review text: The authors consider a general system of discrete (lattice) reaction-diffusion equations with a source term. They prove the existence of a uniform attractor for this system, when the source term is locally square integrable in time, asymptotically small and translation bounded but not translation compact. They show that the family of processes corresponding to the nonautonomous lattice system with source terms belonging to weak closure of translation set of locally asymptotically small functions possesses a uniform attractor, which is also identified with the original attractor. The upper semicontinuity of the uniform attractor is also proved. The paper also contains a review of the recent literature on the existence of uniform attractors in the partial and lattice differential equations.
Mathematics Subject Classification ID: 37L30
Mathematics Subject Classification ID: 37L60
zbMATH DE Number: 5629334
zbMATH Keywords: lattice differential equations
zbMATH Keywords: nonautonomous dynamical systems
zbMATH Keywords: uniform attractors
Wikidata QID: Q59248442
reviewed by: Dmitry Pelinovsky
MaRDI profile type: Publication
OpenAlex ID: W2139974928
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description: scientific article; zbMATH DE number 5629334