Finite Speed of Propagation for the Thin-Film Equation in Spherical Geometry

被引：0
|
作者：
Taranets, R. M. [1 ]
机构：
[1] Ukrainian Natl Acad Sci, Inst Appl Math & Mech, Sloviansk, Ukraine
来源：
UKRAINIAN MATHEMATICAL JOURNAL | 2019年 / 71卷 / 06期
关键词：
NONNEGATIVE SOLUTIONS;
D O I：
10.1007/s11253-019-01690-z
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We show that a doubly degenerate thin-film equation obtained in modeling the flows of viscous coatings on spherical surfaces has a finite speed of propagation for nonnegative strong solutions and, hence, there exists an interface or a free boundary separating the regions, where the solution u > 0 and u = 0. By using local entropy estimates, we also establish the upper bound for the rate of propagation of the interface.
引用
收藏
页码：956 / 969
页数：14
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