WELL-POSEDNESS, REGULARITY AND EXACT CONTROLLABILITY FOR THE PROBLEM OF TRANSMISSION OF THE SCHRODINGER EQUATION

被引：0
|
作者：
Allag, I. [1 ]
Rebiai, S. E. [1 ]
机构：
[1] Univ Batna, Fac Sci, Dept Math, Batna 05000, Algeria
来源：
QUARTERLY OF APPLIED MATHEMATICS | 2014年 / 72卷 / 01期
关键词：
BOUNDARY CONTROL; LINEAR-SYSTEMS; DIRICHLET CONTROL; PLATE EQUATION; WAVE-EQUATION; ELASTICITY;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we shall study the system of transmission of the Schrodinger equation with Dirichlet control and colocated observation. Using the multiplier method, we show that the system is well-posed with input and ouput space U = L-2(Gamma) and state space X = H-1(Omega). The regularity of the system is also established, and the feedthrough operator is found to be zero. Finally, the exact controllability of the open-loop system is obtained by proving the observability inequality of the dual system.
引用
收藏
页码：93 / 108
页数：16
相关论文
共 50 条
  • [41] ON WELL-POSEDNESS OF A MIXED PROBLEM FOR THE WAVE EQUATION
    Gordienko, V. M.
    SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA, 2010, 7 : C130 - C138
  • [42] Well-posedness and energy decay estimates in the Cauchy problem for the damped defocusing Schrodinger equation
    Cavalcanti, Marcelo M.
    Correa, Wellington J.
    Domingos Cavalcanti, Valeria N.
    Tebou, Louis
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2017, 262 (03) : 2521 - 2539
  • [43] Well-posedness for a quadratic derivative nonlinear Schrodinger system at the critical regularity
    Ikeda, Masahiro
    Kishimoto, Nobu
    Okamoto, Mamoru
    JOURNAL OF FUNCTIONAL ANALYSIS, 2016, 271 (04) : 747 - 798
  • [44] Well-posedness and exact controllability of the mass balance equations for an extrusion process
    Diagne, Mamadou
    Shang, Peipei
    Wang, Zhiqiang
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2016, 39 (10) : 2659 - 2670
  • [45] Global Well-posedness for the Defocusing, Quintic Nonlinear Schrodinger Equation in One Dimension for Low Regularity Data
    Dodson, Benjamin G.
    INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2012, 2012 (04) : 870 - 893
  • [46] On the well-posedness of the periodic KdV equation in high regularity classes
    Kappeler, Thomas
    Poeschel, Juergen
    HAMILTONIAN DYNAMICAL SYSTEMS AND APPLICATIONS, 2008, : 431 - +
  • [47] Low regularity well-posedness for the viscous surface wave equation
    Xiaoxia Ren
    Zhaoyin Xiang
    Zhifei Zhang
    Science China Mathematics, 2019, 62 : 1887 - 1924
  • [48] Low regularity well-posedness for the viscous surface wave equation
    Xiaoxia Ren
    Zhaoyin Xiang
    Zhifei Zhang
    ScienceChina(Mathematics), 2019, 62 (10) : 1887 - 1924
  • [49] Well-Posedness and Regularity of Partial Differential Equation Control Systems
    Guo Baozhu
    PROCEEDINGS OF THE 29TH CHINESE CONTROL CONFERENCE, 2010, : 30 - 31
  • [50] Low regularity well-posedness for the viscous surface wave equation
    Ren, Xiaoxia
    Xiang, Zhaoyin
    Zhang, Zhifei
    SCIENCE CHINA-MATHEMATICS, 2019, 62 (10) : 1887 - 1924
12345