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https://hdl.handle.net/10316/11234
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. | URI: | https://hdl.handle.net/10316/11234 | Rights: | openAccess |
Appears in Collections: | FCTUC Matemática - Vários |
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On a doubly nonlinear diffusion model of chemotaxis.pdf | 817.42 kB | Adobe PDF | View/Open |
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