Finite speed of propagation in porous media by mass transportation methods

Abstract In this Note we make use of mass transportation techniques to give a simple proof of the finite speed of propagation of the solution to the one-dimensional porous medium equation. The result follows by showing that the difference of support of any two solutions corresponding to different compactly supported initial data is a bounded in time function of a suitable Monge–Kantorovich related metric. To cite this article: J.A. Carrillo et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).