Math. Model. Nat. Phenom.
Volume 5, Number 3, 2010Mathematical modeling in the medical sciences
|Page(s)||173 - 190|
|Published online||28 April 2010|
On Chemotaxis Models with Cell Population Interactions
Department of Mathematics, University of Vanderbilt, Nashville, TN
This paper extends the volume filling chemotaxis model [18, 26] by taking into account the cell population interactions. The extended chemotaxis models have nonlinear diffusion and chemotactic sensitivity depending on cell population density, which is a modification of the classical Keller-Segel model in which the diffusion and chemotactic sensitivity are constants (linear). The existence and boundedness of global solutions of these models are discussed and the numerical pattern formations are shown. The further improvement is proposed in the end.
Mathematics Subject Classification: 35K55 / 35K57 / 35K61 / 92C15 / 92C17 / 92B99
Key words: chemotaxis / Keller-Segel model / cell interactions / nonlinear diffusion / blow up / volume filling / chemotactic sensitivity / pattern formation
© EDP Sciences, 2010
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