Lagrange multiplier and singular limit of double-obstacle problems for the Allen--Cahn equation with constraint
Lagrange multiplier and singular limit of double-obstacle problems for the Allen--Cahn equation with constraint
复制标题
带约束的Allen--Cahn方程的拉格朗日乘子和双障碍问题的奇异极限
DOI：
10.1002/mma.3905
复制
发表时间：
2017
期刊：
影响因子：
--
通讯作者：
T. Fukao and N. Yamazaki
中科院分区：
文献类型：
--
作者：
M.H. Farshbaf-Shaker;T. Fukao and N. Yamazaki
研究了具有双障碍势的Allen-Cahn方程的拉格朗日乘子的性质。本文研究了动态边界条件，包括边界上的Laplace-Beltrami算子。然后，我们建立了系统的奇异极限，并阐明了问题解的极限和拉格朗日乘子。我们讨论了迹问题和诺依曼边界条件。此外，我们用拉格朗日乘子描述了一个具有诺伊曼边界条件问题的数值实验。版权所有©2016 John Wiley & Sons， Ltd。
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 © 2016 John Wiley & Sons, Ltd.