Special Session 101: Applied Dynamical Systems in Action
Degenerate reaction diffusion systems arising in models for biofilm growth
Stefanie Sonner
Radboud University Netherlands
Co-Author(s): J. Dockery, H.J. Eberl, V. Hissink Muller, J. Hughes, K. Mitra, S. Pop, R. Smeets
Abstract:
Biofilms are dense aggregations of bacterial cells in moist ecosystems that are held together by a self-produced slimy matrix and are often attached to a surface. We consider mathematical models for spatially heterogeneous biofilms that are formulated as quasilinear reaction diffusion systems. Their characteristic feature is the two-fold degenerate diffusion coefficient for the biomass density comprising a polynomial degeneracy (as the porous medium equation) and a fast diffusion singularity as the biomass density approaches its maximum value. This degenerate equation is coupled to semilinear parabolic equations and/or ordinary differential equations for nutrient concentrations and additional substrates. We present results on the well-posedness and regularity of solutions for such systems on bounded and unbounded domains. For systems with immobilized nutrients the existence of traveling wave solutions has been shown. Numerical simulations are presented to illustrate the model behaviour.