Strict contractivity of the 2-Wasserstein distance for the porous medium equation by mass-centering

J. A. Carrillo, M. Di Francesco, G. Toscani

Research output: Contribution to journalArticleResearchpeer-review

21 Citations (Scopus)

Abstract

We show that the Euclidean Wasserstein distance between two compactly supported solutions of the one-dimensional porous medium equation having the same center of mass decays to zero for large times. As a consequence, we detect an improved L1-rate of convergence of solutions of the one-dimensional porous medium equation towards well-centered self-similar Barenblatt profiles, as time goes to infinity. © 2006 American Mathematical Society.
Original languageEnglish
Pages (from-to)353-363
JournalProceedings of the American Mathematical Society
Volume135
Issue number2
DOIs
Publication statusPublished - 1 Feb 2007

Keywords

  • Barenblatt solutions
  • Porous medium equation
  • Wasserstein distance

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