In this paper we prove the null controllability of the heat equation in domains with a cylindrical part and limited by a Lipschitz graph. The proof consists mainly on getting a Carleman estimate which presents the usual absorption properties. The main difficulty we face is the loss of existence of the usual weighted function in C2 smooth domains. In order to deal with this, we use its cylindrical structure and approximate the system by the same system stated in regular domains. Finally, we show some applications like the controllability of the semi-linear heat equation in those domains.
Mots-clés : Carleman inequalities, heat equation, Lipschitz domains, null controllability
@article{COCV_2020__26_1_A122_0,
author = {B\'arcena-Petisco, Jon Asier},
title = {Null controllability of the heat equation in pseudo-cylinders by an internal control},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
publisher = {EDP-Sciences},
volume = {26},
year = {2020},
doi = {10.1051/cocv/2020048},
mrnumber = {4188822},
zbl = {1459.35227},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2020048/}
}
TY - JOUR AU - Bárcena-Petisco, Jon Asier TI - Null controllability of the heat equation in pseudo-cylinders by an internal control JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2020 VL - 26 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2020048/ DO - 10.1051/cocv/2020048 LA - en ID - COCV_2020__26_1_A122_0 ER -
%0 Journal Article %A Bárcena-Petisco, Jon Asier %T Null controllability of the heat equation in pseudo-cylinders by an internal control %J ESAIM: Control, Optimisation and Calculus of Variations %D 2020 %V 26 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2020048/ %R 10.1051/cocv/2020048 %G en %F COCV_2020__26_1_A122_0
Bárcena-Petisco, Jon Asier. Null controllability of the heat equation in pseudo-cylinders by an internal control. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 122. doi : 10.1051/cocv/2020048. http://www.numdam.org/articles/10.1051/cocv/2020048/
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