Search Results
Second-order analysis of a boundary control problem for the viscous Cahn-Hilliard equation with dynamic boundary condition
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.
A boundary control problem for the pure Cahn-Hilliard equation with dynamic boundary 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.
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.
On an application of Tikhonovs fixed point theorem to a nonlocal Cahn-Hilliard type system modeling phase separation
2015, Colli, Pierluigi, Gilardi, Gianni, Sprekels, Jürgen
This paper investigates a nonlocal version of a model for phase separation on an atomic lattice that was introduced by P. Podio-Guidugli in Ric. Mat. 55 (2006) 105-118. The model consists of an initial-boundary value problem for a nonlinearly coupled system of two partial differential equations governing the evolution of an order parameter p and the chemical potential my. Singular contributions to the local free energy in the form of logarithmic or ouble-obstacle potentials are admitted. In contrast to the local model, which was studied by P. Podio-Guidugli and the present authors in a series of recent publications, in the nonlocal case the equation governing the evolution of the order parameter contains in place of the Laplacian a nonlocal expression that originates from nonlocal contributions to the free energy and accounts for possible long-range interactions between the atoms. It is shown that just as in the local case the model equations are well posed, where the technique of proving existence is entirely different: it is based on an application of Tikhonovs fixed point theorem in a rather unusual separable and reflexive Banach space.