Lagrange multiplier and singular limit of double obstacle problems for the Allen-Cahn equation with constraint

被引：1

作者：

Farshbaf-Shaker, Mohammad Hassan ^{[1
]}

Fukao, Takeshi ^{[2
]}

Yamazaki, Noriaki ^{[3
]}

机构：

[1] Weierstrass Inst Appl Anal & Stochast, Mohrenstr 39, D-10117 Berlin, Germany

[2] Kyoto Univ Educ, Dept Math, Fushimi Ku, 1 Fujinomori, Kyoto 6128522, Japan

[3] Kanagawa Univ, Fac Engn, Dept Math, Kanagawa Ku, 3-27-1 Rokkakubashi, Yokohama, Kanagawa 2218686, Japan

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2017年 / 40卷 / 01期

关键词：

Allen-Cahn equation; singular limit; double obstacle; Lagrange multiplier; subdifferential; dynamic boundary condition; PERTURBATIONS; INTERFACES; MOTION;

D O I：

10.1002/mma.3905

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the properties of the Lagrange multiplier for an Allen-Cahn equation with a double obstacle potential. Here, the dynamic boundary condition, including the Laplace-Beltrami operator on the boundary, is investigated. We then establish the singular limit of our system and clarify the limit of the solution and the Lagrange multiplier of our problem. We present remarks on a trace problem as well as on the Neumann boundary condition. Moreover, we describe a numerical experiment for a problem with Neumann boundary condition using the Lagrange multiplier. Copyright (C) 2016 John Wiley & Sons, Ltd.

引用

页码：5 / 21

页数：17

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