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| A problem of singular limit of Allen-Cahn equation with constraint is considered. This problem is modeled by Blowey and Elliott in the 1990s and Chen and Elliott studied the asymptotics, where the constraint of the problem is given by the subdifferential of the indicator function on the closed interval. Bronsard and Kohn (1991) introduced some method for the singular limit of prototype Allen-Cahn equation. The motivation of the research is to apply this method of Bronsard and Kohn to the Allen-Cahn equation with constraint under the Neumann boundary condition, same as Chen and Elliott (1994). This method has an advantage for the numerical analysis. For example, it replaces the large time behavior of the original problem with the sharp interface problem on a short time length. By the characterization of the subdifferential like the Lagrange multiplier, the same kind of result of Bronsard and Kohn (1991) is obtained not only on the Neumann but also the dynamic boundary condition. |
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