On the well‐posedness of a mathematical model of quorum‐sensing in patchy biofilm communities | Zendy

Sonner Stefanie | Zendy; Efendiev Messoud A. | Zendy; Eberl Hermann J. | Zendy

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

Author(s) -

Sonner Stefanie,

Efendiev Messoud A.,

Eberl Hermann J.

Publication year - 2011

Publication title -

mathematical methods in the applied sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.719

H-Index - 65

eISSN - 1099-1476

pISSN - 0170-4214

DOI - 10.1002/mma.1475

Subject(s) - uniqueness , degeneracy (biology) , quorum sensing , mathematics , biofilm , type (biology) , nonlinear system , diffusion , reaction–diffusion system , mathematical analysis , physics , ecology , bacteria , bioinformatics , quantum mechanics , biology , thermodynamics , genetics

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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