论文标题
Lebesgue空间中的Aronson-Bénilan估算值
The Aronson-Bénilan Estimate in Lebesgue Spaces
论文作者
论文摘要
在1979年著名的三页长篇小说中，阿隆森和贝尼兰（Aronson）和贝尼兰（Bénilan）获得了对二阶衍生物的显着估计，用于解决多孔介质方程式。自发表以来，多孔培养基的理论随着热力学，气流，地下水流以及生态种群动态的应用不断扩展。本文的目的是阐明在LP空间中Aronson和Bénilan估算的最新扩展，并进行了一些修改和改进，并显示了其策略的某些局限性。
In a celebrated three-pages long paper in 1979, Aronson and Bénilan obtained a remarkable estimate on second order derivatives for the solution of the porous media equation. Since its publication, the theory of porous medium flow has expanded relentlessly with applications including thermodynamics, gas flow, ground water flow as well as ecological population dynamics. The purpose of this paper is to clarify the use of recent extensions of the Aronson and Bénilan estimate in Lp spaces, of some modifications and improvements, as well as to show certain limitations of their strategy.
