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

• Main Author: Bendahmane, Mostafa
• Publication Date: 2008
• Other Authors: Bürger, Raimund, Baier, Ricardo Ruiz, Urbano, José Miguel
• Format: Other
• Language: eng
• Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
• Download full: https://hdl.handle.net/10316/11234
• topic: Chemotaxis; Reaction-diffusion equations; Degenerate PDE; Parabolic p-Laplacian; Doubly nonlinear; Intrinsic scaling

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.