On the well‐posedness of a mathematical model of quorum‐sensing in patchy biofilm communities |
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| Authors: | Stefanie Sonner Messoud A. Efendiev Hermann J. Eberl |
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| Affiliation: | 1. Institute for Biomathematics and Biometry, Helmholtz Center Munich, Neuherberg, Germany;2. Department of Mathematics and Statistics, University of Guelph, Guelph, Ont., Canada |
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| Abstract: | 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. Copyright © 2011 John Wiley & Sons, Ltd. |
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| Keywords: | biofilm quorum‐sensing degenerate equations well‐posedness |
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