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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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