Geodesic
Controlling linear and semilinear systems formed by one elliptic and two parabolic PDEs with one scalar control
Fernández-Cara, E.1  ; Limaco, J.2 ; de Menezes, S. B.3
1 Dpto. EDAN e IMUS, Universidad de Sevilla, Aptdo. 1160, 41080 Sevilla, Spain.
2 Inst. Matemática, Universidade Federal Fluminense, Valonguinho, 24020-140, Niterói, RJ, Brasil.
3 Dpto. Matemática, Universidade Federal do Ceará, Campus do Pici – Bloco 914, 60455-760, Fortaleza, CE, Brasil.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 4, pp. 1017-1039

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

In this paper, we prove controllability results for some linear and semilinear systems where we find two parabolic PDEs and one elliptic PDE and we act through one locally supported in space scalar control. The arguments rely on a careful analysis of the linear case and an application of an inverse function theorem. The facts that we act through a single scalar control and one of the PDEs has no time derivative are the main novelties and introduce several nontrivial difficulties.

Reçu le :
Accepté le :
DOI : 10.1051/cocv/2016031
Classification : 35B37, 35A05, 35B40
Keywords: Null controllability, parabolic-elliptic linear and semilinear systems, Carleman estimates

Fernández-Cara, E. 1 ; Limaco, J. 2 ; de Menezes, S. B. 3

1 Dpto. EDAN e IMUS, Universidad de Sevilla, Aptdo. 1160, 41080 Sevilla, Spain.
2 Inst. Matemática, Universidade Federal Fluminense, Valonguinho, 24020-140, Niterói, RJ, Brasil.
3 Dpto. Matemática, Universidade Federal do Ceará, Campus do Pici – Bloco 914, 60455-760, Fortaleza, CE, Brasil. 
@article{COCV_2016__22_4_1017_0,
     author = {Fern\'andez-Cara, E. and Limaco, J. and de Menezes, S. B.},
     title = {Controlling linear and semilinear systems formed by one elliptic and two parabolic {PDEs} with one scalar control},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {1017--1039},
     publisher = {EDP-Sciences},
     volume = {22},
     number = {4},
     year = {2016},
     doi = {10.1051/cocv/2016031},
     zbl = {1355.35021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2016031/}
}
TY  - JOUR
AU  - Fernández-Cara, E.
AU  - Limaco, J.
AU  - de Menezes, S. B.
TI  - Controlling linear and semilinear systems formed by one elliptic and two parabolic PDEs with one scalar control
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 2016
SP  - 1017
EP  - 1039
VL  - 22
IS  - 4
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2016031/
DO  - 10.1051/cocv/2016031
LA  - en
ID  - COCV_2016__22_4_1017_0
ER  - 
%0 Journal Article
%A Fernández-Cara, E.
%A Limaco, J.
%A de Menezes, S. B.
%T Controlling linear and semilinear systems formed by one elliptic and two parabolic PDEs with one scalar control
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2016
%P 1017-1039
%V 22
%N 4
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2016031/
%R 10.1051/cocv/2016031
%G en
%F COCV_2016__22_4_1017_0
Fernández-Cara, E.; Limaco, J.; de Menezes, S. B. Controlling linear and semilinear systems formed by one elliptic and two parabolic PDEs with one scalar control. ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 4, pp. 1017-1039. doi: 10.1051/cocv/2016031

Cité par Sources :