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ICCS
2009
Springer

A Nonlinear Master Equation for a Degenerate Diffusion Model of Biofilm Growth

8 years 6 months ago
A Nonlinear Master Equation for a Degenerate Diffusion Model of Biofilm Growth
We present a continuous time/discrete space model of biofilm growth, starting from the semi-discrete master equation. The probabilities of biomass movement into neighboring sites depend on the local biomass density and on the biomass density in the target site such that spatial movement only takes place if (i) locally not enough space is available to accommodate newly produced biomass and (ii) the target site has capacity to accommodate new biomass. This mimics the rules employed by Cellular Automata models of biofilms. Grid refinement leads formally to a degenerate parabolic equation. We show that a set of transition rules can be found such that a previously studied ad hoc density-dependent diffusion-reaction model of biofilm formation is approximated well.
Hassan Khassehkhan, Thomas Hillen, Hermann J. Eber
Added 18 Feb 2011
Updated 18 Feb 2011
Type Journal
Year 2009
Where ICCS
Authors Hassan Khassehkhan, Thomas Hillen, Hermann J. Eberl
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