The Allen–Cahn equation with dynamic boundary conditions and mass constraints |
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Authors: | Pierluigi Colli Takeshi Fukao |
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Affiliation: | 1. Dipartimento di Matematica, Università degli Studi di Pavia, Via Ferrata 1, Pavia, Italy;2. Department of Mathematics, Faculty of Education, Kyoto University of Education, 1 Fujinomori, Fukakusa, Fushimi‐ku, Kyoto, Japan |
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Abstract: | The Allen–Cahn equation, coupled with dynamic boundary conditions, has recently received a good deal of attention. The new issue of this paper is the setting of a rather general mass constraint, which may involve either the solution inside the domain or its trace on the boundary. The system of nonlinear partial differential equations can be formulated as a variational inequality. The presence of the constraint in the evolution process leads to additional terms in the equation and the boundary condition containing a suitable Lagrange multiplier. A well‐posedness result is proved for the related initial value problem. Copyright © 2014 John Wiley & Sons, Ltd. |
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Keywords: | Allen– Cahn equation dynamic boundary condition mass constraint variational inequality Lagrange multiplier |
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