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.
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}, pages = {217--232}, publisher = {Elsevier}, volume = {29}, number = {2}, year = {2012}, doi = {10.1016/j.anihpc.2011.10.003}, mrnumber = {2901195}, zbl = {1276.35106}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2011.10.003/} }
TY - JOUR AU - Takatsu, Asuka TI - Wasserstein geometry of porous medium equation JO - Annales de l'I.H.P. Analyse non linéaire PY - 2012 SP - 217 EP - 232 VL - 29 IS - 2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2011.10.003/ DO - 10.1016/j.anihpc.2011.10.003 LA - en ID - AIHPC_2012__29_2_217_0 ER -
%0 Journal Article %A Takatsu, Asuka %T Wasserstein geometry of porous medium equation %J Annales de l'I.H.P. Analyse non linéaire %D 2012 %P 217-232 %V 29 %N 2 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2011.10.003/ %R 10.1016/j.anihpc.2011.10.003 %G en %F 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/articles/10.1016/j.anihpc.2011.10.003/
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