Analysis of a bacterial model with nutrient-dependent degenerate diffusion

We introduce and study a degenerate reaction-diffusion system that can serve as a model prototype for the pattern formation of a bacterial multicellular community where the bacteria produce biofilm, grow and spread in the presence of a nutrient. Under proper conditions on the reaction terms, we prove the global existence and the uniqueness of solutions and illustrate the possible model behaviour in numerical simulations for a two-dimensional setting.