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.
Sharp rates of decay of solutions to the nonlinear fast diffusion equation via functional inequalities
GRILLO, GABRIELE;
2010-01-01
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.File in questo prodotto:
File | Dimensione | Formato | |
---|---|---|---|
PNAS 2010.pdf
Accesso riservato
:
Post-Print (DRAFT o Author’s Accepted Manuscript-AAM)
Dimensione
213.43 kB
Formato
Adobe PDF
|
213.43 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.