Wasserstein geometry of porous medium equation

Asuka Takatsu

doi:10.1016/j.anihpc.2011.10.003

Wasserstein geometry of porous medium equation

Asuka Takatsu

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	217-232
Number of pages	16
Journal	Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume	29
Issue number	2
DOIs	https://doi.org/10.1016/j.anihpc.2011.10.003
Publication status	Published - 2012
Externally published	Yes

Keywords

Functional inequality
Porous medium equation
q-Gaussian measure

ASJC Scopus subject areas

Analysis
Mathematical Physics
Applied Mathematics

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10.1016/j.anihpc.2011.10.003

Cite this

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title = "Wasserstein geometry of porous medium equation",

abstract = "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 = "Functional inequality, Porous medium equation, q-Gaussian measure",

author = "Asuka Takatsu",

note = "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–IH{\'E}S (EPDI) Fellowship. * Correspondence to: Graduate School of Mathematics, Nagoya University, Nagoya 464-8602, Japan. E-mail address: takatsu@math.nagoya-u.ac.jp.",

year = "2012",

doi = "10.1016/j.anihpc.2011.10.003",

language = "English",

volume = "29",

pages = "217--232",

journal = "Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis",

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publisher = "Elsevier Masson SAS",

number = "2",

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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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DO - 10.1016/j.anihpc.2011.10.003

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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 -

Wasserstein geometry of porous medium equation

Abstract

Keywords

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