On a doubly nonlinear diffusion model of chemotaxis with prevention of overcrow...

• Author(s): Bendahmane, Mostafa ; Bürger, Raimund ; Baier, Ricardo Ruiz ; Urbano, José Miguel
• Date: 2008
• Persistent ID: http://hdl.handle.net/10316/11234
• Origin: Estudo Geral - Universidade de Coimbra
• Subject(s): Chemotaxis; Reaction-diffusion equations; Degenerate PDE; Parabolic p-Laplacian; Doubly nonlinear; Intrinsic scaling
• Document Type: Preprint
• Language: English

Description

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.