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

✍ Scribed by Stefanie Sonner; Messoud A. Efendiev; Hermann J. Eberl

• Publisher: John Wiley and Sons
• Year: 2011
• Tongue: English
• Weight: 563 KB
• Volume: 34
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.1475

✦ Synopsis

Communicated by Q. Wang

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 wellposedness 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.