%0 Journal Article
%T Sharp rates of decay of solutions to the nonlinear fast diffusion equation via functional inequalities
%A Matteo Bonforte
%A Jean Dolbeault
%A Gabriele Grillo
%A Juan-Luis V¨¢zquez
%J Mathematics
%D 2009
%I arXiv
%R 10.1073/pnas.1003972107
%X The goal of this note 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-Poincar\'e inequalities and concludes a long series of papers devoted to generalized entropies, functional inequalities and rates for nonlinear diffusion equations.
%U http://arxiv.org/abs/0907.2986v1