Controllability results for the two-dimensional heat equation with mixed boundary conditions using Carleman inequalities: a linear and a semilinear case

被引：2

作者：

Ziane, Tarik Ali ^{[1
]}

Ouzzane, Hadjer ^{[1
]}

Zair, Ouahiba ^{[1
]}

机构：

[1] USTHB, Lab AMNEDP, Fac Math, Algiers, Algeria

来源：

APPLICABLE ANALYSIS | 2018年 / 97卷 / 14期

关键词：

Mixed boundary conditions; controllability; singularities; Carleman inequalities; semilinear parabolic equations; NULL CONTROLLABILITY; APPROXIMATE CONTROLLABILITY; TRAJECTORIES;

D O I：

10.1080/00036811.2017.1371298

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we prove controllability results for a two-dimensional semilinear heat equation with mixed boundary conditions. It is well-known that mixed boundary conditions can present a singular behaviour of the solution. First, we will prove global Carleman estimates then we will use these inequalities to obtain controllability results.

引用

收藏

页码：2412 / 2430

页数：19

相关论文

共 24 条

[1] PARABOLIC EVOLUTION-EQUATIONS AND NONLINEAR BOUNDARY-CONDITIONS [J].

AMANN, H .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1988, 72 (02) :201-269

[2] Null controllability of nonlinear convective heat equations [J].

Anita, S ;

Barbu, V .

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2000, 5 :157-173

[3]

[Anonymous], 2002, Sci. Math. Jpn.

[4] Parabolic problems with nonlinear boundary conditions and critical nonlinearities [J].

Arrieta, JM ;

Carvalho, AN ;

Rodríguez-Bernal, A .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1999, 156 (02) :376-406

[5] Carleman inequalities for the heat equation in singular domains [J].

Belghazi, Abdelhakim ;

Smadhi, Ferroudja ;

Zaidi, Nawel ;

Zair, Ouahiba .

COMPTES RENDUS MATHEMATIQUE, 2010, 348 (5-6) :277-282

[6] A stability estimate for ill-posed elliptic cauchy problems in a domain with comers [J].

Bourgeois, Laurent .

COMPTES RENDUS MATHEMATIQUE, 2007, 345 (07) :385-390

[7] CARLEMAN ESTIMATES FOR THE ZAREMBA BOUNDARY CONDITION AND STABILIZATION OF WAVES [J].

Cornilleau, Pierre ;

Robbiano, Luc .

AMERICAN JOURNAL OF MATHEMATICS, 2014, 136 (02) :393-444

[8] On the controllability of the heat equation with nonlinear boundary Fourier conditions [J].

Doubova, A ;

Fernández-Cara, E ;

González-Burgos, M .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2004, 196 (02) :385-417

[9] Exact controllability to trajectories for semilinear heat equations with discontinuous diffusion coefficients [J].

Doubova, A ;

Osses, A ;

Puel, JP .

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2002, 8 :621-661

[10] APPROXIMATE CONTROLLABILITY OF THE SEMILINEAR HEAT-EQUATION [J].

FABRE, C ;

PUEL, JP ;

ZUAZUA, E .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1995, 125 :31-61