Semi-wavefront solutions in models of collective movements with density-dependent diffusivity

This paper deals with a nonhomogeneous scalar parabolic equa- tion with possibly degenerate diffusion term; the process has only one station- ary state. The equation can be interpreted as modeling collective movements (crowd dynamics, for instance). We show the existence of semi-wavefront so- lutions for every wave speed; their properties are investigated. Proofs exploit comparison-type techniques and are carried out in the case of one spatial vari- able; the extension to the general case is straightforward.