Lagrange multiplier and singular limit of double obstacle problems for the Allen–Cahn equation with constraint |
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| Authors: | Mohammad Hassan Farshbaf‐Shaker Takeshi Fukao Noriaki Yamazaki |
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| Affiliation: | 1. Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany;2. Department of Mathematics, Kyoto University of Education, Fushimi‐ku, Kyoto, Japan;3. Department of Mathematics, Faculty of Engineering, Kanagawa University, Kanagawa‐ku, Yokohama, JAPAN |
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| Abstract: | 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. |
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| Keywords: | Allen– Cahn equation singular limit double obstacle Lagrange multiplier subdifferential dynamic boundary condition |
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