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

Mostafa Bendahmane, Raimund Burger, Ricardo Ruiz-Baier, José Miguel Urbano, W. Wendland

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


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 and Sons, Ltd.
Original languageEnglish (US)
Pages (from-to)1704-1737
Number of pages34
JournalMathematical Methods in the Applied Sciences
Issue number13
StatePublished - Sep 15 2009
Externally publishedYes

Bibliographical note

Generated from Scopus record by KAUST IRTS on 2023-02-15

ASJC Scopus subject areas

  • General Engineering
  • General Mathematics


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