Degenerate Reaction Diffusion Systems Modeling Biofilm Growth: Well-posedness and Travelling Wave Solutions

Stefanie Sonner (Radboud University Nijmegen) #

Biofilms are dense aggregations of bacterial cells attached to a surface and held together by a self-produced matrix of extracellular polymeric substances. They play a crucial role in natural, medical and industrial settings. We consider continuum models describing the growth of spatially heterogeneous biofilm communities in dependence of growth limiting nutrients. The models are formulated as quasilinear reaction diffusion systems. Their characteristic and challenging feature are the two-fold degenerate diffusion coefficients for the biomass fractions comprising a power-law degeneracy as the biomass density tends to zero (known from the porous medium equation) and a super diffusion singularity as the biomass density approaches its maximum value. We discuss the prototype single species growth model as well as several variations and extensions, with a focus on analytical results. In the second part of the talk, we address a recent model for cellulolytic biofilms. Different from traditional biofilms where the bacterial colonies grow into an aqueous phase and nutrients are transported by diffusion, bacteria colonize, consume and degrade a cellulosic substratum that supports them. Hence, the nutrients are immobilized and modeled by an ordinary differential equation. We show results on the well-posedness of the model and prove the existence of traveling wave solutions. Invading bacterial fronts had earlier been observed in biological experiments on cellulolytic biofilms as well as in numerical simulations of the model. This is joint work with J. Dockery (Montana State University), H. J. Eberl (University of Guelph), V. Hissink Muller (Radboud University), J. Hughes (University of British Columbia) and K. Mitra (Hasselt University).