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.
Accepté le :
DOI : 10.1051/cocv/2016031
Keywords: Null controllability, parabolic-elliptic linear and semilinear systems, Carleman estimates
Fernández-Cara, E. 1 ; Limaco, J. 2 ; de Menezes, S. B. 3
@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},
year = {2016},
publisher = {EDP Sciences},
volume = {22},
number = {4},
doi = {10.1051/cocv/2016031},
zbl = {1355.35021},
language = {en},
url = {https://www.numdam.org/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 - https://www.numdam.org/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 https://www.numdam.org/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
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