Open AccessOptimal distributed control for a coupled phase-field system
Author(s) -
Bosheng Chen,
Huilai Li,
Changchun Liu
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021110
Subject(s) - uniqueness , optimal control , operator (biology) , differentiable function , mathematics , state (computer science) , field (mathematics) , phase (matter) , pure mathematics , control (management) , computer science , control theory (sociology) , mathematical optimization , mathematical analysis , physics , algorithm , quantum mechanics , chemistry , artificial intelligence , biochemistry , repressor , transcription factor , gene
Our aim is to consider a distributed optimal control problem for a coupled phase-field system which was introduced by Cahn and Novick-Cohen. First, we establish that the existence of a weak solution, in particular, we also obtain that a strong solution is uniqueness. Then the existence of optimal controls is proved. Finally we derive that the control-to-state operator is Fréchet differentiable and the first-order necessary optimality conditions involving the adjoint system are discussed as well.