Title: Semi-wavefront solutions in models of collective movements with density-dependent diffusivity,
Abstract: 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 first prove the existence of semi-wavefront
solutions for every wave speed; their properties are investigated. Then, a
family of travelling wave solutions is constructed by a suitable combination of
the previous semi-wavefront solutions. Proofs exploit comparison-type
techniques and are carried out in the case of one spatial variable; the
extension to the general case is straightforward.