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 do...

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Veröffentlicht in:International journal of control Jg. 94; H. 7; S. 1852 - 1869
Hauptverfasser: Colli, Pierluigi, Signori, Andrea
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Abingdon Taylor & Francis 03.07.2021
Taylor & Francis Ltd
Schlagworte:
adjoint problem
Banach spaces
Boundary conditions
Boundary control
Cahn-Hilliard equation
double-well potentials
dynamic boundary conditions
Optimal control
optimality conditions
Optimization
phase separation
ISSN:0020-7179, 1366-5820
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Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0020-7179
1366-5820
DOI:10.1080/00207179.2019.1680870