Second-order analysis of a boundary control problem for the viscous Cahn--Hilliard equation with dynamic boundary condition
- Colli, Pierluigi
- Farshbaf Shaker, Mohammad Hassan
- Gilardi, Gianni
- Sprekels, Jürgen
2010 Mathematics Subject Classification
- 35K55 35K50 82C26
- Cahn--Hilliard equation, dynamic boundary conditions, phase separation, singular potentials, optimal control, first and second order optimality conditions, adjoint state system
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.
- Ann. Acad. Rom. Sci. Math. Appl., 7 (2015) pp. 41--66 .