Global Existence and Convergence Rates for the Strong Solutions in H2 to the 3D Chemotaxis Model

Global Existence and Convergence Rates for the Strong Solutions in H2 to the 3D Chemotaxis Model

We are concerned with a 3D chemotaxis model arising from biology, which is a coupled hyperbolic-parabolic system. We prove the global existence of a strong solution when H2-norm of the initial perturbation around a constant state is sufficiently small. Moreover, if additionally, L1-norm of the initi...

Full description

Bibliographic Details
Main Authors: Weijun Xie, Yinghui Zhang, Yuandong Xiao, Wei Wei
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2013/391056
id doaj-6a14dabe639b405ab1f9d8d2d82205e1
record_format Article
spelling doaj-6a14dabe639b405ab1f9d8d2d82205e12020-11-24T22:28:19ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/391056391056Global Existence and Convergence Rates for the Strong Solutions in H2 to the 3D Chemotaxis ModelWeijun Xie0Yinghui Zhang1Yuandong Xiao2Wei Wei3Department of Primary Education, Hunan National Vocational College, Yueyang, Hunan 414006, ChinaDepartment of Mathematics, Hunan Institute of Science and Technology, Yueyang, Hunan 414006, ChinaDepartment of Mathematics, Hunan Institute of Science and Technology, Yueyang, Hunan 414006, ChinaDepartment of Mathematics, Hunan Institute of Science and Technology, Yueyang, Hunan 414006, ChinaWe are concerned with a 3D chemotaxis model arising from biology, which is a coupled hyperbolic-parabolic system. We prove the global existence of a strong solution when H2-norm of the initial perturbation around a constant state is sufficiently small. Moreover, if additionally, L1-norm of the initial perturbation is bounded; the optimal convergence rates are also obtained for such a solution. The proofs are obtained by combining spectral analysis with energy methods.http://dx.doi.org/10.1155/2013/391056
collection DOAJ
language English
format Article
sources DOAJ
author Weijun Xie
Yinghui Zhang
Yuandong Xiao
Wei Wei
spellingShingle Weijun Xie
Yinghui Zhang
Yuandong Xiao
Wei Wei
Global Existence and Convergence Rates for the Strong Solutions in H2 to the 3D Chemotaxis Model
Journal of Applied Mathematics
author_facet Weijun Xie
Yinghui Zhang
Yuandong Xiao
Wei Wei
author_sort Weijun Xie
title Global Existence and Convergence Rates for the Strong Solutions in H2 to the 3D Chemotaxis Model
title_short Global Existence and Convergence Rates for the Strong Solutions in H2 to the 3D Chemotaxis Model
title_full Global Existence and Convergence Rates for the Strong Solutions in H2 to the 3D Chemotaxis Model
title_fullStr Global Existence and Convergence Rates for the Strong Solutions in H2 to the 3D Chemotaxis Model
title_full_unstemmed Global Existence and Convergence Rates for the Strong Solutions in H2 to the 3D Chemotaxis Model
title_sort global existence and convergence rates for the strong solutions in h2 to the 3d chemotaxis model
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2013-01-01
description We are concerned with a 3D chemotaxis model arising from biology, which is a coupled hyperbolic-parabolic system. We prove the global existence of a strong solution when H2-norm of the initial perturbation around a constant state is sufficiently small. Moreover, if additionally, L1-norm of the initial perturbation is bounded; the optimal convergence rates are also obtained for such a solution. The proofs are obtained by combining spectral analysis with energy methods.
url http://dx.doi.org/10.1155/2013/391056
work_keys_str_mv AT weijunxie globalexistenceandconvergenceratesforthestrongsolutionsinh2tothe3dchemotaxismodel
AT yinghuizhang globalexistenceandconvergenceratesforthestrongsolutionsinh2tothe3dchemotaxismodel
AT yuandongxiao globalexistenceandconvergenceratesforthestrongsolutionsinh2tothe3dchemotaxismodel
AT weiwei globalexistenceandconvergenceratesforthestrongsolutionsinh2tothe3dchemotaxismodel
_version_ 1725746750483857408

Similar Items