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On a doubly nonlinear diffusion model of chemotaxis with prevention of overcrowding

✍ Scribed by Mostafa Bendahmane; Raimund Bürger; Ricardo Ruiz-Baier; José Miguel Urbano

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
599 KB
Volume
32
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

This paper addresses the existence and regularity of weak solutions for a fully parabolic model of chemotaxis, with prevention of overcrowding, that degenerates in a two‐sided fashion, including an extra nonlinearity represented by a p‐Laplacian diffusion term. To prove the existence of weak solutions, a Schauder fixed‐point argument is applied to a regularized problem and the compactness method is used to pass to the limit. The local Hölder regularity of weak solutions is established using the method of intrinsic scaling. The results are a contribution to showing, qualitatively, to what extent the properties of the classical Keller–Segel chemotaxis models are preserved in a more general setting. Some numerical examples illustrate the model. Copyright © 2008 John Wiley & Sons, Ltd.

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