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

Vazquez, Juan-Luis; Grillo, Gabriele; Dolbeault, Jean; Bonforte, Matteo (2010), Sharp rates of decay of solutions to the nonlinear fast diffusion equation via functional inequalities, Proceedings of the National Academy of Sciences of the United States of America, 107, 38, p. 16459-16464. http://dx.doi.org/10.1073/pnas.1003972107

Type
Article accepté pour publication ou publié
External document link
http://arxiv.org/abs/0907.2986v1
Date
2010
Journal name
Proceedings of the National Academy of Sciences of the United States of America
Volume
107
Number
38
Publisher
National Academy of Sciences of the USA
Pages
16459-16464
Publication identifier
Metadata
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Author(s)
Vazquez, Juan-Luis
Grillo, Gabriele
Dolbeault, Jean cc
Bonforte, Matteo
Abstract (EN)
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.
Subjects / Keywords
large-time behavior; Barenblatt solutions; porous media equation; intermediate asymptotics; asymptotic expansion