A free boundary problem with curvature

被引：5
|
作者：
Kim, IC [1 ]
机构：
[1] MIT, Dept Math, Cambridge, MA 02139 USA
来源：
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2005年 / 30卷 / 1-3期
关键词：
comparison principle; free boundary problems; viscosity solutions;
D O I：
10.1081/PDE-200044474
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we are interested in a free boundary problem with a motion law involving the mean curvature term of the free boundary. Viscosity solutions are introduced as a notion of global-time solutions past singularities. We show the comparison principle for viscosity solutions, which yields the existence of minimal and maximal solutions for given initial data. We also prove uniqueness of the solution for several classes of initial data and discuss the possibility of nonunique solutions.
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页码：121 / 138
页数：18
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