A degenerate diffusion-reaction model of an amensalistic biofilm control system: Existence and simulation of solutions

Pages: 371 - 388, Volume 12, Issue 2, September 2009

doi:10.3934/dcdsb.2009.12.371       Abstract        Full Text (1146.0K)       Related Articles

Hassan Khassehkhan - Department of Mathematics and Statistics, University of Guelph, Guelph, On, N1G 2W1, Canada (email)
Messoud A. Efendiev - Institute of Biomathematics and Biometry, HelmholtzZentrum München, Ingolstädter Landstrasse 1, 85764 Neuherberg, Germany (email)
Hermann J. Eberl - Department of Mathematics and Statistics, University of Guelph, Guelph, On, N1G 2W1, Canada (email)

Abstract: We study a mathematical model that describes how a "good" bacterial biofilm controls the growth of a harmful pathogenic bacterial biofilm. The underlying mechanism is a modification of the local protonated acid concentration, which in turn decreases the local pH and, thus, makes growth conditions for the pathogens less favorable, while the control-agent itself is more tolerant to these changes. This system is described by a system of 5 density-dependent diffusion-reaction equations that show two nonlinear diffusion effects: porous medium degeneracy and fast diffusion. This is a multi-species expansion of a previously studied single species biofilm model. In this paper we prove the existence of solutions to this model and show in numerical simulations the effectiveness of the control mechanism.

Keywords:  nonlinear diffusion, degeneracy, biofilm, probiotic, simulation.
Mathematics Subject Classification:  Primary: 35K65; Secondary: 92D25.

Received: September 2008;      Revised: December 2008;      Published: July 2009.