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Strict contractivity of the 2-Wasserstein distance for the porous medium equation by mass-centering |
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| Authors: | J. A. Carrillo M. Di Francesco G. Toscani |
| Affiliation: | Departament de Matemàtiques - ICREA, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Spain ; Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences (ÖAW), A-4040 Linz, Austria ; Dipartimento di Matematica, Università di Pavia, I-27100 Pavia, Italy |
| 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  -rate of convergence of solutions of the one-dimensional porous medium equation towards well-centered self-similar Barenblatt profiles, as time goes to infinity. |
| Keywords: | Porous medium equation Barenblatt solutions Wasserstein distance. |
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