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Optimal control for a phase field system with a possibly singular potential
2014, Colli, Pierluigi, Gilardi, Gianni, Marinoschi, Gabriela, Rocca, Elisabetta
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.
A boundary control problem for the viscous Cahn-Hilliard equation with dynamic boundary conditions
2014, Colli, Pierluigi, Gilardi, Gianni, Sprekels, Jürgen
A boundary control problem for the viscous Cahn-Hilliard equations with possibly singular potentials and dynamic boundary conditions is studied and first order necessary conditions for optimality are proved.