A boundary control problem for the viscous 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 viscous Cahn-Hilliard equation with dynamic boundary conditions, establishing necessary optimality conditions and addressing singular potentials in phase separation modeling.
Contribution
It introduces a novel boundary control framework for the viscous Cahn-Hilliard equation with dynamic boundary conditions, including the derivation of first-order optimality conditions.
Findings
Established necessary conditions for optimal boundary control.
Addressed the handling of singular potentials in the control problem.
Provided insights into phase separation dynamics under boundary control.
Abstract
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. Key words: Cahn-Hilliard equation, dynamic boundary conditions, phase separation, singular potentials, optimal control, optimality conditions, adjoint state system
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