Second-order analysis of a boundary control problem for the viscous Cahn--Hilliard equation with dynamic boundary condition

TL;DR

This paper derives second-order optimality conditions for a boundary control problem involving the viscous Cahn--Hilliard equation with dynamic boundary conditions, extending previous work to include singular potentials.

Contribution

It provides the first second-order sufficient optimality conditions for this class of boundary control problems with dynamic boundary conditions and singular potentials.

Findings

Established second-order optimality conditions for the control problem

Extended analysis to include singular potentials

Enhanced understanding of control problem structure

Abstract

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.