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A degenerate diffusion-reaction model of an amensalistic biofilm control system: Existence and simulation of solutions.
Discrete Contin. Dyn. Syst.-Ser. B 12, 371-388 (2009)
We study a mathematical model that describes how a "good" bacterial biofilm controls the growth of a harmful pathogenic bacterial biofilm. The underlying mechanism is a modification of the local protonated acid concentration, which in turn decreases the local pH and, thus, makes growth conditions for the pathogens less favorable, while the control-agent itself is more tolerant to these changes. This system is described by a system of 5 density-dependent diffusion-reaction equations that show two nonlinear diffusion effects: porous medium degeneracy and fast diffusion. This is a multi-species expansion of a previously studied single species biofilm model. In this paper we prove the existence of solutions to this model and show in numerical simulations the effectiveness of the control mechanism.
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Publication type
Article: Journal article
Document type
Scientific Article
Keywords
nonlinear diffusion; degeneracy; biofilm; probiotic; simulation.
ISSN (print) / ISBN
1531-3492
e-ISSN
1553-524X
Quellenangaben
Volume: 12,
Issue: 2,
Pages: 371-388
Publisher
American Institute of Mathematical Sciences (AIMS)
Non-patent literature
Publications
Reviewing status
Peer reviewed
Institute(s)
Institute of Biomathematics and Biometry (IBB)