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Title: On a doubly nonlinear diffusion model of chemotaxis with prevention of overcrowding
Authors: Bendahmane, Mostafa 
Bürger, Raimund 
Baier, Ricardo Ruiz 
Urbano, José Miguel 
Keywords: Chemotaxis; Reaction-diffusion equations; Degenerate PDE; Parabolic p-Laplacian; Doubly nonlinear; Intrinsic scaling
Issue Date: 2008
Publisher: Centro de Matemática da Universidade de Coimbra
Citation: Pré-Publicações DMUC. 08-41 (2008)
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 fixedpoint argument is applied to a regularized problem and the compactness method is used to pass to the limit. The local H¨older 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.
Rights: openAccess
Appears in Collections:FCTUC Matemática - Vários

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