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

On the well-posedness of mathematical models for multicomponent biofilms.

Math. Meth. Appl. Sci. 38, 3753–3775 (2015)

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

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Bacterial biofilms are microbial depositions on immersed surfaces. Their mathematical description leads to degenerate diffusion-reaction equations with two non-Fickian effects: (i) a porous medium equation like degeneracy where the biomass density vanishes and (ii) a super-diffusion singularity if the biomass density reaches its threshold density. In the case of multispecies interactions, several such equations are coupled, both in the reaction terms and in the nonlinear diffusion operator. In this paper, we generalize previous work on existence and uniqueness of solutions of this type of models and give a general, relatively easy to apply criterion for well-posedness. The use of the criterion is illustrated in several examples from the biofilm modeling literature.

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