Publisher： John Wiley & Sons Inc
E-ISSN： 1099-1476|38|17|3950-3967
ISSN： 0170-4214
Source： MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Vol.38, Iss.17, 2015-11, pp. : 3950-3967
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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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