A Deep Quench Approach to Optimal Control of an Allen-Cahn Equation with Dynamic Boundary Conditions and Double Obstacles

Hassan Farshbaf-Shaker^*, Pierluigi Colli and Jürgen Sprekels

We consider optimal control problems for Allen-Cahn variational inequalities with a dynamic boundary condition involving double obstacles and the Laplace-Beltrami operator. The approach covers both the cases of distributed controls and of boundary controls. The cost functional is of standard tracking type, and box constraints for the controls are prescribed.

Mathematics Subject Classification: 35K15 35R35,49J20, 49K15, 49K20

Keywords: Allen-Cahn system, parabolic obstacle problems, dynamic boundary conditions, optimality conditions, MPECs

Minisymposion: Optimal Control of Time-Dependent Variational Inequalities