  This work describes a hyperbolic model for cell-cell repulsion with
population dynamics. We consider the pressure produced by a population of cells
to describe their motion. We assume that cells try to avoid crowded areas and
prefer locally empty spaces far away from the carrying capacity. Here, our main
goal is to prove the existence of traveling waves with continuous profiles.
This article complements our previous results about sharp traveling waves. We
conclude the paper with numerical simulations of the PDE problem, illustrating
such a result.
