Boundary control problem and optimality conditions for the Cahn–Hilliard equation with dynamic boundary conditions
Year: 2019
Type: article
Abstract: 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 Fréchet differentiability of the control-to-state operator between appropriate Banach spaces, and the first-order necessary conditions for optimality are addressed. In particular, the necessary condition for optimality is characterised by a variational inequality involving the adjoint variables.
Source: International Journal of Control
Authors: Pierluigi Colli, Andrea Signori
Institutions: University of Pavia, University of Milano-Bicocca
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2942778075