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.
|Journal||Proceedings of the American Mathematical Society|
|Publication status||Published - 1 Feb 2007|
- Barenblatt solutions
- Porous medium equation
- Wasserstein distance