Null Controllability of Three-dimensional Heat Equation in Singular Domains

被引：0
作者：
A. H. Belghazi
机构：
[1] U.S.T.H.B,Faculté de mathématiques, Laboratoire AMNEDP
来源：
Acta Applicandae Mathematicae | 2014年 / 134卷
关键词：
Domain with reentrant dihedron; Domain with straight emerging crack; Elliptic operator; Spectral inequality; Carleman estimates; Null controllability; Observability inequality; 95B05; 35J30; 35B65; 35B25; 35J25;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We study in this paper a class of parabolic equations in singular domains. These equations are defined in a singular cylindrical domain whose cross-section contains one reentrant corner or one straight emerging crack. We assume that the diffusion coefficients are non-smooth in the normal direction. We will show some spectral inequality thanks to Carleman type estimates and the construction of a suitable weight function satisfying some properties. As in Benabdallah et al. (C. R. Acad. Sci. Paris 344(6):357–362, 2007), we deduce the null-controllability of these equations with the help of the Lebeau-Robbiano method.
引用
收藏
页码：87 / 109
页数：22
相关论文
共 31 条
[1]  
Bey R.(1999)Singularities of the solution of a mixed problem for a general second order elliptic equation and boundary stabilization of the wave equation J. Math. Pures Appl. 78 1043-1067
[2]  
Lohéac J.P.(2010)Carleman inequalities for the heat equation in singular domains C. R. Acad. Sci. Paris 348 277-282
[3]  
Moussaoui M.(2012)Carleman inequalities for the two dimensional heat equation in singular domains Math. Control Relat. Fields 2 331-359
[4]  
Belghazi A.H.(2007)On the controllability of linear parabolic equations with an arbitrary control location for stratified media C. R. Acad. Sci. Paris 344 357-362
[5]  
Smadhi F.(2010)Discrete Carleman estimates for elliptic operators and uniform controllability of semi-discretized parabolic equations J. Math. Pures Appl. 93 240-276
[6]  
Zair O.(2002)Exact controllability to trajectories for semilinear heat equations with discontinuous diffusion coefficients ESAIM Control Optim. Calc. Var. 8 621-661
[7]  
Zaidi N.(1995)Contrôle exact de l’équation de la chaleur Commun. Partial Differ. Equ. 20 335-356
[8]  
Belghazi A.H.(2007)Carleman estimates and controllability results for the one-dimensional heat equation with BV coefficients J. Differ. Equ. 233 417-447
[9]  
Smadhi F.(1987)Edge behavior of the solution of an elliptic problem Math. Nachr. 132 215-299
[10]  
Zair O.(1989)Contrôlabilité exacte des solutions de l’équation des ondes en présence de singularités J. Math. Pures Appl. 68 215-259
1234