Periodic Traveling Waves of Porous Media Equations with Heterogeneous Reactions

This is the authors' abstract. We don't add key points for this paper.

We consider one dimensional porous media equations with spatially and/or temporally periodic reactions. We construct two kinds of periodic traveling waves. Each of the first kind has a compact support and has average speed (which depends on the reactions and is not too large). The second kind is a periodic traveling semi-wave, that is, its profile is positive on the half line and has a free boundary satisfying the Darcy's law.