A boundary control problem for the pure Cahn-Hilliard equation with dynamic boundary conditions
Pierluigi Colli, Gianni Gilardi, J\"urgen Sprekels
TL;DR
This paper investigates a boundary control problem for the pure Cahn-Hilliard equation with dynamic boundary conditions, establishing necessary optimality conditions for systems with singular potentials.
Contribution
It introduces a novel boundary control framework for the Cahn-Hilliard equation with dynamic boundary conditions and proves first-order optimality conditions.
Findings
Derived first-order necessary optimality conditions.
Handled singular potentials in the control problem.
Extended analysis to dynamic boundary conditions.
Abstract
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. Key words: Cahn-Hilliard equation, dynamic boundary conditions, phase separation, singular potentials, optimal control, optimality conditions
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