A degenerate diffusion-reaction model of an amensalistic biofilm control system: Existence and simulation of solutions
Hassan Khassehkhan - 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.
Received: September 2008; Revised: December 2008; Published: July 2009.
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