Boundary control problem and optimality conditions for the Cahn-Hilliard equation with dynamic boundary conditions

This paper is concerned with a boundary control problem for the Cahn--Hilliard equation coupled with dynamic boundary conditions. In order to handle the control problem, we restrict our analysis to the case of regular potentials defined on the whole real line, assuming the boundary potential to be dominant. The existence of optimal control, the Frechet differentiability of the control-to-state operator between appropriate Banach spaces, and the...