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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
