Publication: Existence and longtime behavior of a biofilm model

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Title	Existence and longtime behavior of a biofilm model
Authors/Editors*	M.A. Efendiev, H.J. Eberl, S.V. Zelik
Where published*	Communications in Pure and Applied Analysis
How published*	Journal
Year*	2008
Volume	in press
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Pages
Publisher
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Abstract	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.