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National Academy of Sciences, Proceedings of the National Academy of Sciences, 38(107), p. 16459-16464

DOI: 10.1073/pnas.1003972107

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Sharp rates of decay of solutions to the nonlinear fast diffusion equation via functional inequalities

Journal article published in 2010 by Matteo Bonforte, Jean Dolbeault ORCID, Gabriele Grillo, Juan-Luis Vazquez
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

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Abstract

The goal of this paper is to state the optimal decay rate for solutions of the nonlinear fast diffusion equation and, in self-similar variables, the optimal convergence rates to Barenblatt self-similar profiles and their generalizations. It relies on the identification of the optimal constants in some related Hardy–Poincaré inequalities and concludes a long series of papers devoted to generalized entropies, functional inequalities, and rates for nonlinear diffusion equations.