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

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.


Published in:
Mathematical Methods in the Applied Sciences, 32, 1704-1737
Year:
2009
Publisher:
Wiley-Blackwell
ISSN:
0170-4214
Keywords:
Laboratories:




 Record created 2009-02-04, last modified 2018-12-03


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