Free-boundary regularity for generalized porous medium equations

被引：10
|
作者：
Daskalopoulos, P [1 ]
Rhee, E
机构：
[1] Columbia Univ, Dept Math, New York, NY 10027 USA
[2] Univ Calif Irvine, Dept Math, Irvine, CA 92717 USA
来源：
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2003年 / 2卷 / 04期
关键词：
generalized porous medium; free-boundary; C-infinity-regularity;
D O I：
10.3934/cpaa.2003.2.481
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the Cauchy problem for the generalized porous medium equation u(t) = DeltaPhi(u) in R-n x [0, T] u(x) = u(0)(x) on R-n with the nonlinearity Phi(u). For the case of Phi(u) = Sigma(i=1)(m) c(i)u(alphai), we show the existence of a solution which smoothness depends on the exponents alpha(i). Regardless of the regularity of the solution, we show the free-boundary is smooth. We also extend similar results for Phi(u) as an infinite sum.
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页码：481 / 494
页数：14
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