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Open Access Green as soon as Postprint is submitted to ZB.
Existence and longtime behavior of a biofilm model.
Commun. Pure Appl. Anal. 8, 509-531 (2009)
A nonlinear, density-dependent system of diffusion-reaction equations describing development of bacterial biofilms is analyzed. It comprises two non-standard diffusion effects, degeneracy as in the porous medium equation and fast diffusion. The existence of a unique bounded solution and a global attractor is proved in dependence of the boundary conditions. This is achieved by studying a system of non-degenerate auxiliary approximation equations and the construction of a Lipschitz continuous semigroup by passing to the limit in the approximation parameter. Numerical examples are included in order to illustrate the main result.
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Publication type
Article: Journal article
Document type
Scientific Article
Keywords
Nonlinear diffusion; degeneracy; global attractor; biofilm
ISSN (print) / ISBN
1534-0392
e-ISSN
1553-5258
Quellenangaben
Volume: 8,
Issue: 2,
Pages: 509-531
Publisher
American Institute of Mathematical Sciences (AIMS)
Non-patent literature
Publications
Reviewing status
Peer reviewed
Institute(s)
Institute of Biomathematics and Biometry (IBB)