Stefanie SonnerRadboud University (Pays-Bas)
Le 21 mars 2024
Titre : Degenerate reaction diffusion systems modeling biofilm growth
Résumé :
Biofilms are dense aggregations of bacterial cells attached to a surface and held together by a self-produced matrix of extracellular polymeric substances. They affect many aspects of human life and play a crucial role in natural, medical and industrial settings. We consider continuum models for spatially heterogeneous biofilm communities 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 a semilinear reaction diffusion equation or an ordinary differential equation for the nutrient concentration. While the first case describes biofilms growing in a liquid phase containing dissolved nutrients, the latter models cellulolytic biofilms where nutrients are immobilized in a cellulose surface on which the biofilm grows.
We present results on the well-posedness and regularity of solutions for such systems on bounded and unbounded domains. For systems with immobilized nutrients we also prove the existence of traveling wave solutions. Such invading fronts had earlier been observed in biological experiments on cellulolytic biofilms as well as in numerical simulations of the model.
