WIAS Preprint No. 2028, (2014)
Optimal control for a phase field system with a possibly singular potential
Authors
- Colli, Pierluigi
ORCID: 0000-0002-7921-5041 - Gilardi, Gianni
ORCID: 0000-0002-0651-4307 - Marinoschi, Gabriela
- Rocca, Elisabetta
ORCID: 0000-0002-9930-907X
2010 Mathematics Subject Classification
- 80A22 35K55 49J20 49K20
Keywords
- Phase field system, phase transition, singular potentials, optimal control, optimality conditions, adjoint state system
DOI
Abstract
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.
Appeared in
- Math. Control Relat. Fields, 6 (2016) pp. 95--112.
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