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Existence and longtime behavior of a biofilm model

Efendiev, MA, Zelik, SV and Eberl, HJ (2009) Existence and longtime behavior of a biofilm model Communications on Pure and Applied Analysis, 8 (2). pp. 509-531.

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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.

Item Type: Article
Subjects : Mathematics
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
AuthorsEmailORCID
Efendiev, MAUNSPECIFIEDUNSPECIFIED
Zelik, SVUNSPECIFIEDUNSPECIFIED
Eberl, HJUNSPECIFIEDUNSPECIFIED
Date : 2009
Identification Number : https://doi.org/10.3934/cpaa.2009.8.509
Copyright Disclaimer : This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Communications on Pure and Applied Analysis following peer review. The definitive publisher-authenticated version COMMUNICATIONS ON PURE AND APPLIED ANALYSIS Volume 8, Number 2, March 2009 doi:10.3934/cpaa.2009.8.509 is available online at: http://aimsciences.org/journals/displayArticles.jsp?paperID=3855
Depositing User : Symplectic Elements
Date Deposited : 03 Nov 2016 14:10
Last Modified : 03 Nov 2016 14:10
URI: http://epubs.surrey.ac.uk/id/eprint/812223

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