Wasserstein geometry of porous medium equation

Asuka Takatsu

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)217-232
Number of pages16
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume29
Issue number2
DOIs
Publication statusPublished - 2012
Externally publishedYes

Keywords

  • Functional inequality
  • Porous medium equation
  • q-Gaussian measure

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics
  • Applied Mathematics

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