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Open Access Green möglich sobald Postprint bei der ZB eingereicht worden ist.
On the well-posedness of mathematical models for multicomponent biofilms.
Math. Meth. Appl. Sci. 38, 3753–3775 (2015)
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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Publikationstyp
Artikel: Journalartikel
Dokumenttyp
Wissenschaftlicher Artikel
Schlagwörter
35k57 ; 92c17 ; 92d25 ; Antibiotic Disinfection ; Biofilm ; Degenerate Reaction-diffusion Systems ; Probiotic Control ; Quorum Sensing ; Subclass35k65 ; Well-posedness
ISSN (print) / ISBN
0170-4214
e-ISSN
1099-1476
Zeitschrift
Mathematical Methods in the Applied Sciences
Quellenangaben
Band: 38,
Heft: 17,
Seiten: 3753–3775
Verlag
Wiley
Nichtpatentliteratur
Publikationen
Begutachtungsstatus
Peer reviewed
Institut(e)
Institute of Computational Biology (ICB)