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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.