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Discrete Dynamics in Nature and Society
Volume 2015, Article ID 143718, 8 pages
http://dx.doi.org/10.1155/2015/143718
Research Article

Global Existence to an Attraction-Repulsion Chemotaxis Model with Fast Diffusion and Nonlinear Source

1Institute of Mathematics, Jilin University, Changchun 130012, China
2Institute of Science, Changchun University, Changchun 130022, China
3Aviation University of Air Force, Changchun 130022, China

Received 7 April 2015; Revised 20 June 2015; Accepted 12 July 2015

Academic Editor: Michael Radin

Copyright © 2015 Yingjie Zhu and Fuzhong Cong. 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

This paper deals with the global existence of solutions to a strongly coupled parabolic-parabolic system of chemotaxis arising from the theory of reinforced random walks. More specifically, we investigate the attraction-repulsion chemotaxis model with fast diffusive term and nonlinear source subject to the Neumann boundary conditions. Such fast diffusion guarantees the global existence of solutions for any given initial value in a bounded domain. Our main results are based on the method of energy estimates, where the key estimates are obtained by a technique originating from Moser’s iterations. Moreover, we notice that the cell density goes to the maximum value when the diffusion coefficient of the cell density tends to infinity.