Eberl, Hermann J.; Parker, David F.; van Loosdrecht, Mark C. M. A new deterministic spatio-temporal continuum model for biofilm development. (English) Zbl 0985.92009 J. Theor. Med. 3, No. 3, 161-175 (2001). Summary: A new mathematical model for the development of spatially heterogeneous biofilm structures is presented. Unlike previous hybrid discrete/continuum models it is a continuum model throughout, describing the interaction of nutrient availability and biomass production. Spatial biomass spreading is described by a nonlinear density-dependent diffusion mechanism. The diffusion operator degenerates for small biomass densities and is singular at the biomass density bound. The model can be interpreted as a predator-prey model for biomass and nutrients. First numerical simulations show that the model is able to predict experimentally observed cluster-and-channel biofilm structures. The results are reliable and in qualitatively good agreement with experimental expectations. Cited in 64 Documents MSC: 92C05 Biophysics 92D40 Ecology 65C20 Probabilistic models, generic numerical methods in probability and statistics 35Q92 PDEs in connection with biology, chemistry and other natural sciences Keywords:biofilms; spatio-temporal mathematical modelling PDFBibTeX XMLCite \textit{H. J. Eberl} et al., J. Theor. Med. 3, No. 3, 161--175 (2001; Zbl 0985.92009) Full Text: DOI EuDML