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

Bonforte, M; Dolbeault, J; Grillo, G; Vázquez, J L · Proc Natl Acad Sci U S A · 2010

basic_science · Level V

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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.