CONVERGENCE OF THE ALLEN-CAHN EQUATION WITH NEUMANN BOUNDARY CONDITIONS

被引：29

作者：

Mizuno, Masashi ^{[1
]}

Tonegawa, Yoshihiro ^{[2
]}

机构：

[1] Nihon Univ, Coll Sci & Technol, Dept Math, Tokyo 1018308, Japan

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

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2015年 / 47卷 / 03期

关键词：

boundary monotonicity formula; Allen-Cahn equation; mean curvature flow; varifold; MEAN-CURVATURE FLOW; GENERALIZED MOTION; PHASE-TRANSITIONS; INTERFACES; DIFFUSION; PROPAGATION;

D O I：

10.1137/140987808

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study a singular limit problem of the Allen-Cahn equation with Neumann boundary conditions and general initial data of uniformly bounded energy. We prove that the time-parametrized family of limit energy measures is Brakke's mean curvature flow with a generalized right angle condition on the boundary.

引用

页码：1906 / 1932

页数：27

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