EVENTUAL C-INFINITY-REGULARITY AND CONCAVITY FOR FLOWS IN ONE-DIMENSIONAL POROUS-MEDIA

被引：43

作者：

ARONSON, DG ^{[1
]}

VAZQUEZ, JL ^{[1
]}

机构：

[1] UNIV AUTONOMA MADRID,DIV MATEMAT,MADRID 34,SPAIN

来源：

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 1987年 / 99卷 / 04期

关键词：

FLUID MECHANICS - Mathematical Models;

D O I：

10.1007/BF00282050

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the regularity and the asymptotic behavior of the solutions of the initial value problem for the porous medium equation with m greater than 1 and, u//0 a continuous, nonnegative function. We prove that each moving part of the interface is a C** infinity -curve and that upsilon is C** infinity on each side of the moving interface (and up to it). We also prove that for solutions with compact support the pressure becomes a concave function of chi after a finite time. This fact implies sharp convergence rates for the solution and the interfaces as t yields infinity .

引用

页码：329 / 348

页数：20