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Eberl, H.J.* ; Efendiyev, M.A. ; Wrzosek, D.* ; Zhigun, A.*

Analysis of a degenerate biofilm model with a nutrient taxis term.

Discrete Contin. Dyn. Syst.-Ser. A 34, 99-119 (2014)
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We introduce and analyze a prototype model for chemotactic effects in biofilm formation. The model is a system of quasilinear parabolic equations into which two thresholds are built in. One occurs at zero cell density level, the second one is related to the maximal density which the cells cannot exceed. Accordingly, both diffusion and taxis terms have degenerate or singular parts. This model extends a previously introduced degenerate biofilm model by combining it with a chemotaxis equation. We give conditions for existence and uniqueness of weak solutions and illustrate the model behavior in numerical simulations.
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Publication type Article: Journal article
Document type Scientific Article
Keywords Chemotaxis ; Biofilm ; Degenerate Diffusion ; Fast Diffusion ; Singular Quasilinear Parabolic Equation ; Compactness Method; Singularity Formation ; Chemotaxis Model ; Diffusion
ISSN (print) / ISBN 1078-0947
e-ISSN 1553-5231
Quellenangaben Volume: 34, Issue: 1, Pages: 99-119 Article Number: , Supplement: ,
Publisher American Institute of Mathematical Sciences (AIMS)
Reviewing status