Geodesic
Wasserstein geometry of porous medium equation
Annales de l'I.H.P. Analyse non linéaire, Tome 29 (2012) no. 2, pp. 217-232

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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.

DOI : 10.1016/j.anihpc.2011.10.003
Classification : 60D05, 46E27
Keywords: q-Gaussian measure, Porous medium equation, Functional inequality 
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     title = {Wasserstein geometry of porous medium equation},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {217--232},
     publisher = {Elsevier},
     volume = {29},
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     year = {2012},
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Takatsu, Asuka. Wasserstein geometry of porous medium equation. Annales de l'I.H.P. Analyse non linéaire, Tome 29 (2012) no. 2, pp. 217-232. doi: 10.1016/j.anihpc.2011.10.003

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