Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/5914
Title: Global regularity versus infinite-time singularity formation in a chemotaxis model with volume-filling effect and degenerate diffusion
Authors: Wang, Z 
Winkler, M
Wrzosek, D
Keywords: Chemotaxis
Volume filling
Singular diffusion
Degenerate diffusion
Singularity formation
Issue Date: 2012
Publisher: Society for Industrial and Applied Mathematics
Source: SIAM journal on mathematical analysis, 2012, v. 44, no. 5, p. 3502-3525 How to cite?
Journal: SIAM Journal on mathematical analysis 
Abstract: A system of quasi-linear parabolic and elliptic-parabolic equations describing chemotaxis is studied. Due to the assumed presence of a volume-filling effect it is assumed that there is an impassable threshold for the density of cells. This assumption leads to singular or degenerate operators in both the diffusive and the chemotactic components of the flux of cells. We improve results from earlier works and find critical conditions which reflect the interplay between diffusion and chemotaxis and warrant that classical solutions are global in time and separated uniformly from the threshold. In the case of degenerate diffusion for the elliptic-parabolic version of the model we prove the existence of radially symmetric solutions which exhibit a phenomenon of infinite-time singularity formation in that they are global and smooth but attain the threshold in the large time limit.
URI: http://hdl.handle.net/10397/5914
ISSN: 0036-1410 (print)
1095-7154 (online)
DOI: 10.1137/110853972
Rights: © 2012 Society for Industrial and Applied Mathematics
Appears in Collections:Journal/Magazine Article

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