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