Optimal distributed control of the Cahn–Hilliard–Brinkman system with regular potential. (May 2019)

• Record Type: Journal Article
• Authors: You, Bo; Li, Fang
• Is Part Of: Nonlinear analysis. Volume 182(2019)
• Page Start: 226
• Page End: 247
• Publication Date: 2019-05
• Subjects: 49J20 -- 49J50 -- 49K20 -- 92C50; Distributed optimal control -- First-order necessary optimality conditions -- Cahn–Hilliard–Brinkman system -- Adjoint state system -- Phase separation; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2018.12.014
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: The main objective of this paper is to study the optimal distributed control of the three dimensional Cahn–Hilliard–Brinkman system with regular potential. We apply recently proved well-posedness and regularity results in order to establish the existence of optimal controls as well as the first-order necessary optimality conditions for an associated optimal control problem in which a distributed control is applied to the fluid flow.