Departamento de Matemáticas, Universidad Autónoma de Madrid, Campus de Cantoblanco, 28049 Madrid, Spain.
Proc Natl Acad Sci U S A. 2010 Sep 21;107(38):16459-64. doi: 10.1073/pnas.1003972107. Epub 2010 Sep 7.
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.
本文的目的是给出非线性快速扩散方程解的最优衰减率，并在自相似变量下给出最优收敛率到 Barenblatt 自相似轮廓及其推广。它依赖于在一些相关的 Hardy-Poincaré 不等式中确定最优常数，并总结了一系列致力于广义熵、泛函不等式和非线性扩散方程速率的论文。
