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A boundary control problem for the pure Cahn–Hilliard equation with dynamic boundary conditions
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.
Second-order analysis of a boundary control problem for the viscous Cahn-Hilliard equation with dynamic boundary condition
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
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.
A boundary control problem for the viscous Cahn-Hilliard equation with dynamic boundary conditions
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.