  Motivated by models for biofilm growth, we consider Cauchy problems for
quasilinear reaction diffusion equations where the diffusion coefficient has a
porous medium type degeneracy as well as a singularity. We prove results on the
well-posedness and Sobolev regularity of solutions. The proofs are based on
m-accretive operator theory, kinetic formulations and Fourier analytic
techniques.
