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Journal of Applied Mathematics
Volume 2013, Article ID 391056, 9 pages
http://dx.doi.org/10.1155/2013/391056
Research Article

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

1Department of Primary Education, Hunan National Vocational College, Yueyang, Hunan 414006, China
2Department of Mathematics, Hunan Institute of Science and Technology, Yueyang, Hunan 414006, China
3The Hubei Key Laboratory of Mathematical Physics, School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China

Received 5 September 2013; Accepted 7 November 2013

Academic Editor: K. S. Govinder

Copyright © 2013 Weijun Xie et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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 -norm of the initial perturbation around a constant state is sufficiently small. Moreover, if additionally, -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.