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 |
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Pages (from-to) | 353-363 |
Journal | Proceedings of the American Mathematical Society |
Volume | 135 |
Issue number | 2 |
DOIs | |
Publication status | Published - 1 Feb 2007 |
Keywords
- Barenblatt solutions
- Porous medium equation
- Wasserstein distance