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

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 : https://doi.org/10.1016/j.anihpc.2011.10.003
Classification:  60D05,  46E27
Keywords: q-Gaussian measure, Porous medium equation, Functional inequality
@article{AIHPC_2012__29_2_217_0,
     author = {Takatsu, Asuka},
     title = {Wasserstein geometry of porous medium equation},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {29},
     number = {2},
     year = {2012},
     pages = {217-232},
     doi = {10.1016/j.anihpc.2011.10.003},
     zbl = {1276.35106},
     mrnumber = {2901195},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2012__29_2_217_0}
}
Takatsu, Asuka. Wasserstein geometry of porous medium equation. Annales de l'I.H.P. Analyse non linéaire, Volume 29 (2012) no. 2, pp. 217-232. doi : 10.1016/j.anihpc.2011.10.003. http://www.numdam.org/item/AIHPC_2012__29_2_217_0/

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