Regularity of Global Attractor for the Reaction-Diffusion Equation

Regularity of Global Attractor for the Reaction-Diffusion Equation

By using an iteration procedure, regularity estimates for the linear semigroups, and a classical existence theorem of global attractor, we prove that the reaction-diffusion equation possesses a global attractor in Sobolev space Hk for all k>0, which attracts any bounded subset of Hk(Ω) in the Hk-...

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Main Author: Hong Luo
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2012/917190
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spelling doaj-c3c24831798e494b935a7406076fa6052020-11-24T22:28:51ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/917190917190Regularity of Global Attractor for the Reaction-Diffusion EquationHong Luo0College of Mathematics and Software Science, Sichuan Normal University, Sichuan, Chengdu 610066, ChinaBy using an iteration procedure, regularity estimates for the linear semigroups, and a classical existence theorem of global attractor, we prove that the reaction-diffusion equation possesses a global attractor in Sobolev space Hk for all k>0, which attracts any bounded subset of Hk(Ω) in the Hk-norm.http://dx.doi.org/10.1155/2012/917190
collection DOAJ
language English
format Article
sources DOAJ
author Hong Luo
spellingShingle Hong Luo
Regularity of Global Attractor for the Reaction-Diffusion Equation
Abstract and Applied Analysis
author_facet Hong Luo
author_sort Hong Luo
title Regularity of Global Attractor for the Reaction-Diffusion Equation
title_short Regularity of Global Attractor for the Reaction-Diffusion Equation
title_full Regularity of Global Attractor for the Reaction-Diffusion Equation
title_fullStr Regularity of Global Attractor for the Reaction-Diffusion Equation
title_full_unstemmed Regularity of Global Attractor for the Reaction-Diffusion Equation
title_sort regularity of global attractor for the reaction-diffusion equation
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2012-01-01
description By using an iteration procedure, regularity estimates for the linear semigroups, and a classical existence theorem of global attractor, we prove that the reaction-diffusion equation possesses a global attractor in Sobolev space Hk for all k>0, which attracts any bounded subset of Hk(Ω) in the Hk-norm.
url http://dx.doi.org/10.1155/2012/917190
work_keys_str_mv AT hongluo regularityofglobalattractorforthereactiondiffusionequation
_version_ 1725746048490536960

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