Qualitative behavior and traveling waves for flux-saturated porous media equations arising in optimal mass transportation

This paper is devoted to the analysis of qualitative properties of porous media flux-saturated type operators which combine the effects of reaction terms of FKPP-type in dimension one. Specifically, we study the existence of traveling wave profiles, sub- and super-solutions, waiting time and dynamical properties of the support. The paper also deals with the connection between these minimal traveling waves with those of other related models: Porous media, flux saturated mechanism, and the heat equation.