Abstract
In this paper we deal with some optimal control problems for a solidification phase field model of metallic alloys. The model allows crystallizations of two kinds, each one described by its own phase field. Accordingly, the state is the triplet (τ,u,v), where τ is the temperature and u and v are phase field functions. The optimality conditions for the optimal control problems considered in this work are obtained by using the Dubovitskii-Milyutin formalism.
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E. Fernández-Cara partially supported by grant MTM2006–07932 of the D.G.I. (Spain).
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Boldrini, J.L., Caretta, B.M.C. & Fernández-Cara, E. Some optimal control problems for a two-phase field model of solidification. Rev Mat Complut 23, 49–75 (2010). https://doi.org/10.1007/s13163-009-0012-0
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DOI: https://doi.org/10.1007/s13163-009-0012-0
- Solidification
- Phase field models
- Parabolic partial differential equations
- Optimal control
- Dubovitskii-Milyutin formalism