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On Chemotaxis Models with Cell Population Interactions

Published online by Cambridge University Press:  28 April 2010

Z. A. Wang
Z. A. Wang*
Affiliation:
Department of Mathematics, University of Vanderbilt, Nashville, TN 37240
*
* E-mail:zhian.wang@vanderbilt.edu
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Abstract

This paper extends the volume filling chemotaxis model [18, 26] by taking into account the cell population interactions. Theextended chemotaxis models have nonlinear diffusion and chemotactic sensitivity dependingon cell population density, which is a modification of the classical Keller-Segel model inwhich the diffusion and chemotactic sensitivity are constants (linear). The existence andboundedness of global solutions of these models are discussed and the numerical patternformations are shown. The further improvement is proposed in the end.

Keywords

chemotaxisKeller-Segel modelcell interactionsnonlinear diffusionblow upvolume fillingchemotactic sensitivitypattern formation
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 5 , Issue 3: Mathematical modeling in the medical sciences , 2010 , pp. 173 - 190
Copyright
© EDP Sciences, 2010

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