A Nonlinear Master Equation for a Degenerate Diffusion Model of Biofilm Growth
作者： Hassan Khassehkhan , Thomas Hillen , Hermann J Eberl
DOI: 10.1007/978-3-642-01970-8_73
关键词: Mathematical analysis 、 Nonlinear system 、 Grid 、 Cellular automaton 、 Discrete space 、 Degenerate energy levels 、 Space (mathematics) 、 Mathematics 、 Master equation 、 Biomass 、 Biological system
摘要: We present a continuous time/discrete space model of biofilm growth, starting from the semi-discrete master equation. The probabilities biomass movement into neighboring sites depend on local density and in target site such that spatial only takes place if (i) locally not enough is available to accommodate newly produced (ii) has capacity new biomass. This mimics rules employed by Cellular Automata models biofilms. Grid refinement leads formally degenerate parabolic show set transition can be found previously studied ad hoc density-dependent diffusion-reaction formation approximated well.
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