Null controllability of the heat equation with boundary Fourier conditions:: The linear case

被引：79
|
作者：
Fernandez-Cara, Enrique [1 ]
Gonzalez-Burgos, Manuel
Guerrero, Sergio
Puel, Jean-Pierre
机构：
[1] Univ Sevilla, Dpto EDAN, E-41080 Seville, Spain
[2] Univ Paris 06, Lab Jacques Louis Lions, F-75035 Paris 05, France
[3] Univ Versailles, Lab Math Appl, F-78035 Versailles, France
来源：
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2006年 / 12卷 / 03期
关键词：
controllability; heat equation; Fourier conditions;
D O I：
10.1051/cocv:2006010
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
In this paper, we prove the global null controllability of the linear heat equation completed with linear Fourier boundary conditions of the form partial derivative y/partial derivative n + beta y = 0. We consider distributed controls with support in a small set and nonregular coefficients beta = beta(x, t). For the proof of null controllability, a crucial tool will be a new Carleman estimate for the weak solutions of the classical heat equation with nonhomogeneous Neumann boundary conditions.
引用
收藏
页码：442 / 465
页数：24
相关论文
共 50 条
  • [1] BOUNDARY NULL CONTROLLABILITY FOR THE HEAT EQUATION WITH DYNAMIC BOUNDARY CONDITIONS
    Chorfi, Salah-Eddine
    EL Guermai, Ghita
    Khoutaibi, Abdelaziz
    Maniar, Lahcen
    [J]. EVOLUTION EQUATIONS AND CONTROL THEORY, 2023, 12 (02): : 542 - 566
  • [2] NULL CONTROLLABILITY FOR A HEAT EQUATION WITH PERIODIC BOUNDARY CONDITIONS
    Oner, Isil
    [J]. UNIVERSITY POLITEHNICA OF BUCHAREST SCIENTIFIC BULLETIN-SERIES A-APPLIED MATHEMATICS AND PHYSICS, 2021, 83 (04): : 13 - 22
  • [3] On the controllability of the heat equation with nonlinear boundary Fourier conditions
    Doubova, A
    Fernández-Cara, E
    González-Burgos, M
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2004, 196 (02) : 385 - 417
  • [4] NULL CONTROLLABILITY FOR SEMILINEAR HEAT EQUATION WITH DYNAMIC BOUNDARY CONDITIONS
    Khoutaibi, Abdelaziz
    Maniar, Lahcen
    Oukdach, Omar
    [J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2022, 15 (06): : 1525 - 1546
  • [5] Exact controllability to the trajectories of the heat equation with Fourier boundary conditions:: The semilinear case
    Fernandez-Cara, Enrique
    Gonzalez-Burgos, Manuel
    Guerrero, Sergio
    Puel, Jean-Pierre
    [J]. ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2006, 12 (03) : 466 - 483
  • [6] Null controllability of a linear KdV equation on an interval with special boundary conditions
    Guilleron, Jean-Philippe
    [J]. MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS, 2014, 26 (03) : 375 - 401
  • [7] Null controllability of a linear KdV equation on an interval with special boundary conditions
    Jean-Philippe Guilleron
    [J]. Mathematics of Control, Signals, and Systems, 2014, 26 : 375 - 401
  • [8] IMPULSE NULL APPROXIMATE CONTROLLABILITY FOR HEAT EQUATION WITH DYNAMIC BOUNDARY CONDITIONS
    Chorfi, Salah-Eddine
    El Guermai, Ghita
    Maniar, Lahcen
    Zouhair, Walid
    [J]. MATHEMATICAL CONTROL AND RELATED FIELDS, 2023, 13 (03) : 1023 - 1046
  • [9] NULL CONTROLLABILITY FOR A HEAT EQUATION WITH DYNAMIC BOUNDARY CONDITIONS AND DRIFT TERMS
    Khoutaibi, Abdelaziz
    Maniar, Lahcen
    [J]. EVOLUTION EQUATIONS AND CONTROL THEORY, 2020, 9 (02): : 535 - 559
  • [10] The null boundary controllability for the Mullins equation with periodic boundary conditions
    Oner, Isil
    [J]. INTERNATIONAL JOURNAL OF OPTIMIZATION AND CONTROL-THEORIES & APPLICATIONS-IJOCTA, 2023, 13 (01): : 116 - 122
12345