This paper is devoted to the study of the internal null-controllability of the Grushin equation. We determine the minimal time of controllability for a large class of non-rectangular control regions. We establish the positive result thanks to the fictitious control method and the negative one by interpreting the associated observability inequality as an L2 estimate on complex polynomials.
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DOI : 10.1051/cocv/2019001
Mots-clés : Controllability, minimal time, degenerated parabolic equations
@article{COCV_2020__26_1_A3_0,
author = {Duprez, Michel and Koenig, Armand},
title = {Control of the {Grushin} equation: non-rectangular control region and minimal time},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
publisher = {EDP-Sciences},
volume = {26},
year = {2020},
doi = {10.1051/cocv/2019001},
mrnumber = {4050579},
zbl = {1447.93025},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2019001/}
}
TY - JOUR AU - Duprez, Michel AU - Koenig, Armand TI - Control of the Grushin equation: non-rectangular control region and minimal time JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2020 VL - 26 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2019001/ DO - 10.1051/cocv/2019001 LA - en ID - COCV_2020__26_1_A3_0 ER -
%0 Journal Article %A Duprez, Michel %A Koenig, Armand %T Control of the Grushin equation: non-rectangular control region and minimal time %J ESAIM: Control, Optimisation and Calculus of Variations %D 2020 %V 26 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2019001/ %R 10.1051/cocv/2019001 %G en %F COCV_2020__26_1_A3_0
Duprez, Michel; Koenig, Armand. Control of the Grushin equation: non-rectangular control region and minimal time. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 3. doi : 10.1051/cocv/2019001. http://www.numdam.org/articles/10.1051/cocv/2019001/
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Cité par Sources :
The first author was partially supported by the Project “Analysis and simulation of optimal shapes – application to life sciences” of the Paris City Hall.
The second author was partially supported by the ERC advanced grant SCAPDE, seventh framework program, agreement no. 320845.
