Abstract

Biofilms are dense aggregations of bacterial cells attached to a surface and held together by a self-produced slimy matrix. We consider 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 a semilinear parabolic equation or an ordinary differential equation for the nutrient concentration. 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.