Geodesic
Null controllability of the heat equation with boundary Fourier conditions : the linear case
Fernández-Cara, Enrique  ; González-Burgos, Manuel  ; Guerrero, Sergio1  ; Puel, Jean-Pierre2 
1 Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, boîte courrier 187, 75035 Cedex 05, Paris, France;
2 Laboratoire de Mathématiques Appliquées, Université de Versailles – St. Quentin, 45 avenue des États-Unis, 78035 Versailles, France; ; Laboratoire de Mathématiques Appliquées, Université de Versailles, St. Quentin, 45 avenue des États-Unis, 78035 Versailles, France;
ESAIM: Control, Optimisation and Calculus of Variations, Tome 12 (2006) no. 3, pp. 442-465

Voir la notice de l'article provenant de la source Numdam

In this paper, we prove the global null controllability of the linear heat equation completed with linear Fourier boundary conditions of the form ∂y ∂n+βy=0. We consider distributed controls with support in a small set and nonregular coefficients β=β(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.

DOI : 10.1051/cocv:2006010
Classification : 35K20, 93B05
Keywords: controllability, heat equation, Fourier conditions

Fernández-Cara, Enrique  ; González-Burgos, Manuel  ; Guerrero, Sergio 1 ; Puel, Jean-Pierre 2

1 Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, boîte courrier 187, 75035 Cedex 05, Paris, France;
2 Laboratoire de Mathématiques Appliquées, Université de Versailles – St. Quentin, 45 avenue des États-Unis, 78035 Versailles, France; ; Laboratoire de Mathématiques Appliquées, Université de Versailles, St. Quentin, 45 avenue des États-Unis, 78035 Versailles, France; 
@article{COCV_2006__12_3_442_0,
     author = {Fern\'andez-Cara, Enrique and Gonz\'alez-Burgos, Manuel and Guerrero, Sergio and Puel, Jean-Pierre},
     title = {Null controllability of the heat equation with boundary {Fourier} conditions : the linear case},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {442--465},
     publisher = {EDP-Sciences},
     volume = {12},
     number = {3},
     year = {2006},
     doi = {10.1051/cocv:2006010},
     mrnumber = {2224822},
     zbl = {1106.93009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2006010/}
}
TY  - JOUR
AU  - Fernández-Cara, Enrique
AU  - González-Burgos, Manuel
AU  - Guerrero, Sergio
AU  - Puel, Jean-Pierre
TI  - Null controllability of the heat equation with boundary Fourier conditions : the linear case
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 2006
SP  - 442
EP  - 465
VL  - 12
IS  - 3
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/cocv:2006010/
DO  - 10.1051/cocv:2006010
LA  - en
ID  - COCV_2006__12_3_442_0
ER  - 
%0 Journal Article
%A Fernández-Cara, Enrique
%A González-Burgos, Manuel
%A Guerrero, Sergio
%A Puel, Jean-Pierre
%T Null controllability of the heat equation with boundary Fourier conditions : the linear case
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2006
%P 442-465
%V 12
%N 3
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/cocv:2006010/
%R 10.1051/cocv:2006010
%G en
%F COCV_2006__12_3_442_0
Fernández-Cara, Enrique; González-Burgos, Manuel; Guerrero, Sergio; Puel, Jean-Pierre. Null controllability of the heat equation with boundary Fourier conditions : the linear case. ESAIM: Control, Optimisation and Calculus of Variations, Tome 12 (2006) no. 3, pp. 442-465. doi: 10.1051/cocv:2006010

Cité par Sources :