On the existence of mean curvature flow with transport term

被引：13

作者：

Liu, Chun ^{[1
]}

Sato, Norifumi ^{[2
]}

Tonegawa, Yoshihiro ^{[3
]}

机构：

[1] Univ Minnesota, IMA, Minneapolis, MN 55455 USA

[2] Furano HS, Furano, Hokkaido 0760011, Japan

[3] Hokkaido Univ, Dept Math, Sapporo, Hokkaido 0600810, Japan

来源：

INTERFACES AND FREE BOUNDARIES | 2010年 / 12卷 / 02期

关键词：

Mean curvature flow; varifold; Allen-Cahn equation; phase field method; FREE-BOUNDARY PROBLEM; ALLEN-CAHN EQUATION; MOTION; CONVERGENCE; REGULARITY; SETS;

D O I：

10.4171/IFB/234

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove the global-in-time existence of weak solution for a hypersurface evolution problem where the velocity is the sum of the mean curvature and arbitrarily given non-smooth vector field in a suitable Sobolev space. The approximate solution is obtained by the Allen-Cahn equation with transport term. By establishing the density ratio upper bound on the phase boundary measure it is shown that the limiting surface moves with the desired velocity in the sense of Brakke.

引用

页码：251 / 277

页数：27

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