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

被引：68

作者：

Bonforte, M. ^{[1
]}

Dolbeault, J. ^{[2
]}

Grillo, G. ^{[3
]}

Vazquez, J. L. ^{[1
,4
]}

机构：

[1] Univ Autonoma Madrid, Dept Matemat, E-28049 Madrid, Spain

[2] Univ Paris 09, CEREMADE, UMR 7534, Ctr Natl Rech Sci, F-75775 Paris 16, France

[3] Politecn Milan, Dipartimento Matemat, I-20133 Milan, Italy

[4] Univ Autonoma Madrid, Inst Ciencias Matemat, E-28049 Madrid, Spain

来源：

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA | 2010年 / 107卷 / 38期

关键词：

asymptotic expansion; intermediate asymptotics; porous media equation; Barenblatt solutions; large-time behavior; POROUS-MEDIUM EQUATION; POINCARE INEQUALITIES; ASYMPTOTIC-BEHAVIOR; EVOLUTION; ENTROPY;

D O I：

10.1073/pnas.1003972107

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

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-Poincare inequalities and concludes a long series of papers devoted to generalized entropies, functional inequalities, and rates for nonlinear diffusion equations.

引用

页码：16459 / 16464

页数：6

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