Optimal bilinear control of nonlinear Schrodinger equations with singular potentials

被引：4
作者：
Feng, Binhua [1 ,2 ]
Zhao, Dun [2 ]
Chen, Pengyu [1 ]
机构：
[1] Northwest Normal Univ, Dept Math, Lanzhou 730070, Peoples R China
[2] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Peoples R China
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2014年 / 107卷
基金：
中央高校基本科研业务费专项资金资助; 中国国家自然科学基金;
关键词：
Optimal bilinear control; Nonlinear Schrodinger equation; Optimal condition; Singular potentials; CONTROLLABILITY; STABILIZATION; MANIFOLDS;
D O I：
10.1016/j.na.2014.04.017
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider an optimal bilinear control problem for the nonlinear Schrodinger equations with singular potentials. We show the well-posedness of the problem and the existence of an optimal control. In addition, the first order optimality system is rigorously derived. Our results give an improvement for some recent results. (C) 2014 Elsevier Ltd. All rights reserved.
引用
收藏
页码：12 / 21
页数：10
相关论文
共 28 条
  • [1] [Anonymous], 1971, OPTIMAL CONTROL SYST
  • [2] [Anonymous], 2007, Mathematical Surveys and Monographs
  • [3] [Anonymous], 2004, LONDON MATH SOC LECT
  • [4] Regularity for a Schrodinger equation with singular potentials and application to bilinear optimal control
    Baudouin, L
    Kavian, O
    Puel, JP
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2005, 216 (01) : 188 - 222
  • [5] Constructive solution of a bilinear optimal control problem for a Schrodinger equation
    Baudouin, Lucie
    Salomon, Julien
    [J]. SYSTEMS & CONTROL LETTERS, 2008, 57 (06) : 453 - 464
  • [6] Controllability of a quantum particle in a moving potential well
    Beauchard, K
    Coron, JM
    [J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2006, 232 (02) : 328 - 389
  • [7] Local controllability of 1D linear and nonlinear Schrodinger equations with bilinear control
    Beauchard, Karine
    Laurent, Camille
    [J]. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2010, 94 (05): : 520 - 554
  • [8] Nonadiabatic control of Bose-Einstein condensation in optical traps
    Bulatov, A
    Vugmeister, BE
    Rabitz, H
    [J]. PHYSICAL REVIEW A, 1999, 60 (06): : 4875 - 4881
  • [9] Geometric control in the presence of a black box
    Burq, N
    Zworski, M
    [J]. JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2004, 17 (02) : 443 - 471
  • [10] Cazenave T, 2003, Semilinear Schrodinger Equations
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