TY - JOUR
T1 - Wasserstein geometry of porous medium equation
AU - Takatsu, Asuka
N1 - Funding Information:
✩ This work was partially supported by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists and by JSPS–IHÉS (EPDI) Fellowship. * Correspondence to: Graduate School of Mathematics, Nagoya University, Nagoya 464-8602, Japan. E-mail address: takatsu@math.nagoya-u.ac.jp.
PY - 2012
Y1 - 2012
N2 - 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.
AB - 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.
KW - Functional inequality
KW - Porous medium equation
KW - q-Gaussian measure
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U2 - 10.1016/j.anihpc.2011.10.003
DO - 10.1016/j.anihpc.2011.10.003
M3 - Article
AN - SCOPUS:84858700460
VL - 29
SP - 217
EP - 232
JO - Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis
JF - Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis
SN - 0294-1449
IS - 2
ER -