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

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

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

Strict contractivity of the 2-Wasserstein distance for the porous medium equation by mass-centering
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by J. A. Carrillo, M. Di Francesco and G. Toscani

Proc. Amer. Math. Soc. 135 (2007), 353-363

DOI: https://doi.org/10.1090/S0002-9939-06-08594-7

Published electronically: August 21, 2006

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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 $L^1$–rate of convergence of solutions of the one–dimensional porous medium equation towards well–centered self–similar Barenblatt profiles, as time goes to infinity.

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