Optimal boundary control of a phase field system modeling nonisothermal phase transitions
- Lefter, Catalin
- Sprekels, Jürgen
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.
- Adv. Math. Sci. Appl., 17 (2007) pp. 181-194.