2014, Colli, Pierluigi, Farshbaf Shaker, Mohammad Hassan, Gilardi, Gianni, Sprekels, Jürgen

In this paper we establish second-order sufficient optimality conditions for a boundary control problem that has been introduced and studied by three of the authors in the preprint arXiv:1407.3916. This control problem regards the viscous Cahn-Hilliard equation with possibly singular potentials and 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.

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.

2015, Colli, Pierluigi, Gilardi, Gianni, Sprekels, Jürgen

A boundary control problem for the pure Cahn-Hilliard equations with possibly singular potentials and dynamic boundary conditions is studied and first-order necessary conditions for optimality are proved.