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Sonner, S. ; Efendiyev, M.A. ; Eberl, H.J.*

On the well-posedness of a mathematical model of quorum-sensing in patchy biofilm communities.

Math. Meth. Appl. Sci. 34, 1667-1684 (2011)

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Open Access Green as soon as Postprint is submitted to ZB.

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We analyze a system of reaction-diffusion equations that models quorum-sensing in a growing biofilm. The model comprises two nonlinear diffusion effects: a porous medium-type degeneracy and super diffusion. We prove the well-posedness of the model. In particular, we present for the first time a uniqueness result for this type of problem. Moreover, we illustrate the behavior of model solutions in numerical simulations.

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Publication type Article: Journal article

Document type Scientific Article

Corresponding Author

Keywords biofilm; quorum-sensing; degenerate equations; well-posedness

ISSN (print) / ISBN 0170-4214

e-ISSN 1099-1476

Journal Mathematical Methods in the Applied Sciences

Quellenangaben Volume: 34, Issue: 13, Pages: 1667-1684

Publisher Wiley

Non-patent literature Publications

Reviewing status Peer reviewed

Institute(s) Institute of Biomathematics and Biometry (IBB)