The geometry of dissipative evolution equations: The porous medium equation

被引：896
作者：
Otto, F [1 ]
机构：
[1] Univ Calif Santa Barbara, Dept Math, Santa Barbara, CA 93106 USA
来源：
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2001年 / 26卷 / 1-2期
关键词：
D O I：
10.1081/PDE-100002243
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We show that the porous medium equation has a gradient flow structure which is both physically and mathematically natural. In order to convince the reader that it is mathematically natural, we show that the time asymptotic behavior can be easily understood in this framework. We use the intuition and the calculus of Riemannian geometry to quantify this asymptotic behavior.
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页码：101 / 174
页数：74
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