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IMA Journal of Mathematical Control and Information 1993 10(2):157-176; doi:10.1093/imamci/10.2.157
© 1993 by Institute of Mathematics and its Applications
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Optimal boundary controls for a phase field model

ZHIMING CHEN

Institute of Applied Mathematics and Statistics, Technical University of Munich Dachauerstr. 9a, 8000 Munich 2, Germany

The phase field model is a nonlinear system of parabolic equations which describes the phase transitions between two different phases, e.g. solid and liquid. In this paper, we consider a general optimal boundary control problem which is governed by this model. The existence of the solutions of the phase field model is established by a rigorous analysis of the method of lines. The existence of the optimal solutions and the necessary conditions for optimality are proved. For a special unconstrained boundary control problem, we also prove some results concerning the uniqueness of the optimal solutions. For a special constrained boundary control problem, we obtain a result concerning the bang-bang principle.


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