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 -