Internal layers intersecting the boundary of domain in the Allen-Cahn equation

被引：4

作者：

Iibun, T ^{[1
]}

Sakamoto, K

机构：

[1] Hiroshima Univ, Grad Sch Sci, Dept Math, Higashihiroshima 7398526, Japan

[2] Hiroshima Univ, Grad Sch Sci, Inst Nonlinear Sci & Appl Math, Higashihiroshima 7398526, Japan

来源：

JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS | 2001年 / 18卷 / 03期

关键词：

internal layers; the Allen-Cahn equation; mean curvature flow; singular perturbation; asymptotic expansion;

D O I：

10.1007/BF03167411

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For the Allen-Cahn equation with balanced nonlinearity, we show the existence of equilibrium internal layers intersecting the boundary of two dimensional bounded smooth domains. Stability analysis is carried out for the layers and local shape of the boundary is classified according to the stability of the layers. Numerical simulations are exhibited which indicate that bifurcations occur as the domain boundary is perturbed.

引用

页码：697 / 738

页数：42

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