Optimal control for a phase field system with a possibly singular potential

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.

Keywords

Phase field system, phase transition, singular potentials, optimal control, optimality conditions, adjoint state system

URI

https://doi.org/10.34657/2936
https://oa.tib.eu/renate/handle/123456789/2897

Citation

Colli, P., Gilardi, G., Marinoschi, G., & Rocca, E. (2014). Optimal control for a phase field system with a possibly singular potential. Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.

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Mathematik

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