Local null controllability of a free-boundary problem for the viscous Burgers equation

被引：0
|
作者：
Fernández-Cara E. [1 ]
De Sousa I.T. [2 ]
机构：
[1] Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Aptdo. 1160, Seville
[2] Departamento de Matemática, Universidade Federal do Ceará, Fortaleza, CE
来源：
SeMA Journal | 2017年 / 74卷 / 4期
关键词：
Burgers equations; Carleman estimates; Controllability; Free-boundary;
D O I：
10.1007/s40324-016-0092-y
中图分类号：
学科分类号：
摘要：
We analyze the null controllability of a 1D nonlinear system which models the interaction of a fluid and its boundary. The fluid is governed by the viscous Burgers equation and the distributed controls, locally supported in space. We present two main results: the approximate controllability of a linearized system and the local null controllability of the nonlinear original model. The proofs rely on appropriate global Carleman inequalities, observability estimates and fixed point arguments. © 2016, Sociedad Española de Matemática Aplicada.
引用
收藏
页码：411 / 427
页数：16
相关论文
共 50 条
  • [1] Local Null Controllability of a Free-Boundary Problem for the Semilinear 1D Heat Equation
    Enrique Fernández-Cara
    Ivaldo Tributino de Sousa
    [J]. Bulletin of the Brazilian Mathematical Society, New Series, 2017, 48 : 303 - 315
  • [2] Local Null Controllability of a Free-Boundary Problem for the Semilinear 1D Heat Equation
    Fernandez-Cara, Enrique
    de Sousa, Ivaldo Tributino
    [J]. BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, 2017, 48 (02): : 303 - 315
  • [3] Local null controllability of a free-boundary problem for the quasi-linear 1D parabolic equation
    Wang, Lili
    Lan, Yuzhen
    Lei, Peidong
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2022, 506 (02)
  • [4] AN OBSTRUCTION TO SMALL-TIME LOCAL NULL CONTROLLABILITY FOR A VISCOUS BURGERS' EQUATION
    Marbach, Frederic
    [J]. ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE, 2018, 51 (05): : 1129 - 1177
  • [5] On the Controllability of a Free-Boundary Problem for 1D Heat Equation with Local and Nonlocal Nonlinearities
    V. Costa
    J. Límaco
    A. R. Lopes
    L. Prouvée
    [J]. Applied Mathematics & Optimization, 2023, 87
  • [6] THE WELL-POSEDNESS OF A FREE-BOUNDARY PROBLEM FOR BURGERS-EQUATION
    BERTSCH, M
    HILHORST, D
    SCHMIDTLAINE, C
    [J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1994, 23 (09) : 1211 - 1224
  • [7] On the Controllability of a Free-Boundary Problem for 1D Heat Equation with Local and Nonlocal Nonlinearities
    Costa, V
    Limaco, J.
    Lopes, A. R.
    Prouvee, L.
    [J]. APPLIED MATHEMATICS AND OPTIMIZATION, 2023, 87 (01):
  • [8] Small time global null controllability for a viscous Burgers' equation despite the presence of a boundary layer
    Marbach, Frederic
    [J]. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2014, 102 (02): : 364 - 384
  • [9] On the controllability of a free-boundary problem for the 1D heat equation
    Fernandez-Cara, E.
    Limaco, J.
    de Menezes, S. B.
    [J]. SYSTEMS & CONTROL LETTERS, 2016, 87 : 29 - 35
  • [10] Local exact Lagrangian controllability of the Burgers viscous equation
    Horsin, Thierry
    [J]. ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2008, 25 (02): : 219 - 230
12345