Geodesic
Exact controllability to the trajectories of the heat equation with Fourier boundary conditions : the semilinear 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. 466-483

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

This paper is concerned with the global exact controllability of the semilinear heat equation (with nonlinear terms involving the state and the gradient) completed with boundary conditions of the form ∂y ∂n+f(y)=0. We consider distributed controls, with support in a small set. The null controllability of similar linear systems has been analyzed in a previous first part of this work. In this second part we show that, when the nonlinear terms are locally Lipschitz-continuous and slightly superlinear, one has exact controllability to the trajectories.

DOI : 10.1051/cocv:2006011
Classification : 35K20, 93B05
Keywords: controllability, heat equation, Fourier boundary conditions, semilinear

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_466_0,
     author = {Fern\'andez-Cara, Enrique and Gonz\'alez-Burgos, Manuel and Guerrero, Sergio and Puel, Jean-Pierre},
     title = {Exact controllability to the trajectories of the heat equation with {Fourier} boundary conditions : the semilinear case},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {466--483},
     publisher = {EDP-Sciences},
     volume = {12},
     number = {3},
     year = {2006},
     doi = {10.1051/cocv:2006011},
     mrnumber = {2224823},
     zbl = {1106.93010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2006011/}
}
TY  - JOUR
AU  - Fernández-Cara, Enrique
AU  - González-Burgos, Manuel
AU  - Guerrero, Sergio
AU  - Puel, Jean-Pierre
TI  - Exact controllability to the trajectories of the heat equation with Fourier boundary conditions : the semilinear case
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 2006
SP  - 466
EP  - 483
VL  - 12
IS  - 3
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/cocv:2006011/
DO  - 10.1051/cocv:2006011
LA  - en
ID  - COCV_2006__12_3_466_0
ER  - 
%0 Journal Article
%A Fernández-Cara, Enrique
%A González-Burgos, Manuel
%A Guerrero, Sergio
%A Puel, Jean-Pierre
%T Exact controllability to the trajectories of the heat equation with Fourier boundary conditions : the semilinear case
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2006
%P 466-483
%V 12
%N 3
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/cocv:2006011/
%R 10.1051/cocv:2006011
%G en
%F COCV_2006__12_3_466_0
Fernández-Cara, Enrique; González-Burgos, Manuel; Guerrero, Sergio; Puel, Jean-Pierre. Exact controllability to the trajectories of the heat equation with Fourier boundary conditions : the semilinear case. ESAIM: Control, Optimisation and Calculus of Variations, Tome 12 (2006) no. 3, pp. 466-483. doi: 10.1051/cocv:2006011

Cité par Sources :