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An optimal control problem for a singular system of solid-liquid phase transition. (English) Zbl 1214.80004

The authors of this work deal with a control problem for a phase field system that describes a solid-liquid phase transition by the Ginzburg-Landau theory. They start the paper with a detailed derivation of a phase field system of nonlinear partial differential equations involving the temperature and the phase field variables. This section is followed by the formulation of the control problem. The purpose of the control problem is to guide the system into a certain state (solid, liquid) on a part of the domain through determination of the heat supply and maintain the system in this state during a specific time period. An approximating control problem is introduced next and this is followed by a section that includes a proof of the existence of a solution. First order optimality conditions are given in the next section. The last section contains results on the convergence of solutions of the approximating problem to the original control problem.

MSC:

80A22 Stefan problems, phase changes, etc.
49J20 Existence theories for optimal control problems involving partial differential equations
35Q56 Ginzburg-Landau equations
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