title: Sharp rates of decay of solutions to the nonlinear fast diffusion equation via functional inequalities.
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.
authors.affiliation: Departamento de Matemáticas, Universidad Autónoma de Madrid, Campus de Cantoblanco, 28049 Madrid, Spain.
authors.forename: M
authors.initials: M
authors.lastname: Bonforte
authors.forename: J
authors.initials: J
authors.lastname: Dolbeault
authors.forename: G
authors.initials: G
authors.lastname: Grillo
authors.forename: J L
authors.initials: JL
authors.lastname: Vázquez
references.citation: Proc Natl Acad Sci U S A. 2003 Jun 10;100(12):6922-5
references.pmid: 12766227