Analysis of propagating fronts in a nonlinear diffusion model with chemotaxis

This work is devoted to the study of traveling wave front solutions of a phenomenological model for pattering in bacterial colonies which incorporates cell movements in a nonlinear diffusion and chemotaxis. An analysis of propagating fronts in the model is performed to describe the occurrence of a sharp front with a minimum speed, as well as smooth fronts. This analysis also leads us to construct the sharp front profiles and accurately determine their minimum speed. Moreover, numerical time-dependent solutions of the model are constructed to confirm the results of the analysis.

► We study a nonlinear diffusion model with chemotaxis.
► We analyze the problem of propagating front in the model.
► We compute accurately a sharp front with a minimum speed.
► We use different numerical methods.