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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Authors: J. A. Carrillo, M. Di Francesco and G. Toscani
Journal: Proc. Amer. Math. Soc. 135 (2007), 353-363
MSC (2000): Primary 35K65; Secondary 35B40
Published electronically: August 21, 2006
MathSciNet review: 2255281
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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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Additional Information

J. A. Carrillo
Affiliation: Departament de Matemàtiques - ICREA, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Spain
Email: carrillo@mat.uab.es

M. Di Francesco
Affiliation: Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences (ÖAW), A-4040 Linz, Austria
Address at time of publication: Sezione di Matematica per L’Ingegneria, Universita di L’Aquila, Piazzale Pontieri, Monteluco di Roio, I-67100 L’Aquila, Italy
Email: marco.difrancesco@oeaw.ac.at

G. Toscani
Affiliation: Dipartimento di Matematica, Università di Pavia, I-27100 Pavia, Italy
Email: giuseppe.toscani@unipv.it

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08594-7
PII: S 0002-9939(06)08594-7
Keywords: Porous medium equation, Barenblatt solutions, Wasserstein distance.
Received by editor(s): July 27, 2005
Published electronically: August 21, 2006
Communicated by: Walter Craig
Article copyright: © Copyright 2006 American Mathematical Society