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

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

doi:10.1090/S0002-9939-06-08594-7

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

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

Department of Mathematics

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

20 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 language	English
Pages (from-to)	353-363
Journal	Proceedings of the American Mathematical Society
Volume	135
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9939-06-08594-7
Publication status	Published - 1 Feb 2007

Keywords

Barenblatt solutions
Porous medium equation
Wasserstein distance

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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. {\textcopyright} 2006 American Mathematical Society.",

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AB - 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.

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KW - Porous medium equation

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