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

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• 作者：Mohammad Hassan Farshbaf-Shaker ; Takeshi Fukao and Noriaki Yamazaki
• 刊名：Mathematical Methods in the Applied Sciences
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：40
• 期：1
• 页码：5-21
• 全文大小：1123K
• ISSN：1099-1476

文摘

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