WIAS Preprint No. 1187, (2006)

Optimal boundary control of a phase field system modeling nonisothermal phase transitions


  • Lefter, Catalin
  • Sprekels, Jürgen
    ORCID: juergen.sprekels@wias-berlin.de

2010 Mathematics Subject Classification

  • 49K20 35K55 80A22 49J20


  • Phase-field system, phase transition, optimal control, necessary conditions




In this paper, we study an optimal control problem for a singular system of partial differential equations that models a nonisothermal phase transition with a nonconserved order parameter. The control acts through a third boundary condition for the absolute temperature and plays the role of the outside temperature. It is shown that the corresponding control-to-state mapping is well defined, and the existence of an optimal control and the first-order optimality conditions for a quadratic cost functional of Bolza type are established.

Appeared in

  • Adv. Math. Sci. Appl., 17 (2007) pp. 181-194.

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