WIAS Preprint No. 2028, (2014)

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


  • 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


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




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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