Distributed and boundary optimal control of the Allen–Cahn equation with regular potential and dynamic boundary conditions
Cargando...
Archivos
Fecha
2016
Título de la revista
Publicado en
International Journal of Control, 1366-5820, Vol 89, Nro 8, 2016, p 1523-1532
Publicado por
Taylor and Francis
ISSN de la revista
Título del volumen
Resumen
Descripción
Abstract
This paper is concerned with an optimal control problem (P) (both distributed control as well as boundary control) for the nonlinear phase-field (Allen–Cahn) equation, involving a regular potential and dynamic boundary condition. A family of approximate optimal control problems (Pϵ) is introduced and results for the existence of an optimal control for problems (P) and (Pϵ) are proven. Furthermore, the convergence result of the optimal solution of problem (Pϵ) to the optimal solution of problem (P) is proved. Besides the existence of an optimal control in problem (Pϵ), necessary optimality conditions (Pontryagin's principle) as well as a conceptual gradient-type algorithm to approximate the optimal control, were established in the end.
Palabras clave
Keywords
Boundary value problems for nonlinear parabolic PDE, Dynamic boundary conditions, Pontryagin's maximum principle, Fractional steps method, Phase changes