  A nonlinear PDE featuring flux limitation effects together with those of the
porous media equation (nonlinear Fokker-Planck) is presented in this paper. We
analyze the balance of such diverse effects through the study of the existence
and qualitative behavior of some admissible patterns, namely traveling wave
solutions, to this singular reaction-difusion equation. We show the existence
and qualitative behavior of different types of traveling waves: classical
profiles for wave speeds high enough, and discontinuous waves that are
reminiscent of hyperbolic shock waves when the wave speed lowers below a
certain threshold. Some of these solutions are of particular relevance as they
provide models by which the whole solution (and not just the bulk of it, as it
is the case with classical traveling waves) spreads through the medium with
finite speed.
