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Optimal control for a phase field system with a possibly singular potential. (English) Zbl 1335.49008
Summary: In this paper, we study a distributed control problem for a phase field system of Caginalp type with logarithmic potential. The main aim of this work would be to force the location of the diffuse interface to be as close as possible to a prescribed set. However, due to the discontinuous character of the cost functional, we have to approximate it by a regular one and, in this case, we solve the associated control problem and derive the related first order necessary optimality conditions.

MSC:
49J20 Existence theories for optimal control problems involving partial differential equations
49K20 Optimality conditions for problems involving partial differential equations
35K55 Nonlinear parabolic equations
80A22 Stefan problems, phase changes, etc.
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