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

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