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

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

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

In this paper, we investigate optimal boundary control problems for Cahn--Hilliard variational inequalities with a dynamic boundary condition involving double obstacle potentials and the Laplace--Beltrami operator. The cost functional is of standard tracking type, and box constraints for the controls are prescribed. We prove existence of optimal controls and derive first-order necessary conditions of optimality. The general strategy, which follows the lines of the recent approach by Colli, Farshbaf-Shaker, Sprekels (see Appl. Math. Optim., 2014) to the (simpler) Allen--Cahn case, is the following: we use the results that were recently established by Colli, Gilardi, Sprekels in the preprint arXiv:1407.3916 [math.AP] for the case of (differentiable) logarithmic potentials and perform a so-called ``deep quench limit''. Using compactness and monotonicity arguments, it is shown that this strategy leads to the desired first-order necessary optimality conditions for the case of (non-differentiable) double obstacle potentials.

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.

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.

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.