Wasserstein geometry of porous medium equation

  • Asuka Takatsu

    Graduate School of Mathematics, Nagoya University, Nagoya 464-8602, Japan, Institut des Hautes Études Scientifiques, Bures-sur-Yvette 91440, France, Max-Planck-Intitut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany


We study the porous medium equation with emphasis on q-Gaussian measures, which are generalizations of Gaussian measures by using power-law distribution. On the space of q-Gaussian measures, the porous medium equation is reduced to an ordinary differential equation for covariance matrix. We introduce a set of inequalities among functionals which gauge the difference between pairs of probability measures and are useful in the analysis of the porous medium equation. We show that any q-Gaussian measure provides a nontrivial pair attaining equality in these inequalities.

Cite this article

Asuka Takatsu, Wasserstein geometry of porous medium equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 29 (2012), no. 2, pp. 217–232

DOI 10.1016/J.ANIHPC.2011.10.003