Optimal Control Problem for the Cahn-Hilliard/Allen-Cahn Equation with State Constraint

被引：14
|
作者：
Zhang, Xiaoli [1 ]
Li, Huilai [1 ]
Liu, Changchun [1 ]
机构：
[1] Jilin Univ, Dept Math, Changchun 130012, Peoples R China
来源：
APPLIED MATHEMATICS AND OPTIMIZATION | 2020年 / 82卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Cahn-Hilliard; Allen-Cahn equation; State constraint; Optimal control; Optimality conditions; Adjoint state system; LONG-TIME BEHAVIOR; WELL-POSEDNESS; SYSTEM; EXISTENCE;
D O I：
10.1007/s00245-018-9546-1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider a distributed optimal control problem for the Cahn-Hilliard/Allen-Cahn equation with state-constraint. The objective is to force the coverageyto have some specified properties or achieve a certain goal. Since the cost functional is discontinuous, together with state constraint, we employ a new penalty functional by the approximation of the cost functional, in this case, we derive the necessary optimality conditions for the approximating optimal control problem. Finally, by considering the limits of the necessary optimality conditions we have obtained, we solve the optimal control problem and derive the necessary optimality conditions.
引用
收藏
页码：721 / 754
页数：34
相关论文
共 50 条
  • [1] Optimal Control Problem for the Cahn–Hilliard/Allen–Cahn Equation with State Constraint
    Xiaoli Zhang
    Huilai Li
    Changchun Liu
    Applied Mathematics & Optimization, 2020, 82 : 721 - 754
  • [2] ON THE EXISTENCE OF SOLUTION FOR A CAHN-HILLIARD/ALLEN-CAHN EQUATION
    Karali, Georgia
    Nagase, Yuko
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2014, 7 (01): : 127 - 137
  • [3] Global Dynamics of the Cahn-Hilliard/Allen-Cahn Equation
    Ma, Mingze
    Zhao, Xiaopeng
    JOURNAL OF MATHEMATICAL STUDY, 2023, 56 (02) : 156 - 172
  • [4] Optimal Distributed Control of a Allen-Cahn/Cahn-Hilliard System with Temperature
    Chen, Bosheng
    Liu, Changchun
    APPLIED MATHEMATICS AND OPTIMIZATION, 2021, 84 (SUPPL 2): : 1639 - 1684
  • [5] The Cahn-Hilliard/Allen-Cahn equation with inertial and proliferation terms
    Sen, Zehra
    Khanmamedov, Azer
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2024, 530 (02)
  • [6] THE EXISTENCE OF GLOBAL ATTRACTOR FOR A CAHN-HILLIARD/ALLEN-CAHN EQUATION
    Tang, H.
    Liu, C.
    Zhao, Z.
    BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2016, 42 (03): : 643 - 658
  • [7] The Cahn-Hilliard Equation and the Allen-Cahn Equation on Manifolds with Conical Singularities
    Roidos, Nikolaos
    Schrohe, Elmar
    COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2013, 38 (05) : 925 - 943
  • [8] ON THE STEADY STATE BIFURCATION OF THE CAHN-HILLIARD/ALLEN-CAHN SYSTEM
    Li, Shixing
    Yan, Dongming
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2019, 24 (07): : 3077 - 3088
  • [9] Optimal Control Problem for Cahn-Hilliard Equations with State Constraint
    Zheng, Jiashan
    Wang, Yifu
    JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS, 2015, 21 (02) : 257 - 272
  • [10] EXISTENCE OF SOLUTIONS TO THE CAHN-HILLIARD/ALLEN-CAHN EQUATION WITH DEGENERATE MOBILITY
    Zhang, Xiaoli
    Liu, Changchun
    ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2016,
12345