[Contrôle simultané de l’équation de la chaleur avec conditions aux limites de Dirichlet et Neumann]
It is well known that both the heat equation with Dirichlet or Neumann boundary conditions are null controlable as soon as the control acts in a non trivial domain (i.e. a set of positive measure). In this article, we show that for any couple of initial data we can achieve the null control for both equations (Dirichlet and Neumann boundary conditions respectively) simultaneously with the same control function for both equations.
Il est bien connu que l’équation de la chaleur avec aussi bien la condition au bord de Dirichlet que la condition de Neumann est contrôlable à dès que le contrôle agit sur un domain non trivial (i.e. de mesure positive). Dans cet article, nous montrons que pour tout couple de données initiales , le contrôle à peut être réalisé simultanément avec la même fonction de contrôle pour les deux équations.
Révisé le :
Accepté le :
Publié le :
Burq, Nicolas 1 ; Moyano, Ivan 2
CC-BY 4.0
@article{CRMATH_2024__362_G9_937_0,
author = {Burq, Nicolas and Moyano, Ivan},
title = {Simultaneous control for the heat equation with {Dirichlet} and {Neumann} boundary conditions},
journal = {Comptes Rendus. Math\'ematique},
pages = {937--942},
year = {2024},
publisher = {Acad\'emie des sciences, Paris},
volume = {362},
number = {G9},
doi = {10.5802/crmath.535},
language = {en},
url = {https://www.numdam.org/articles/10.5802/crmath.535/}
}
TY - JOUR AU - Burq, Nicolas AU - Moyano, Ivan TI - Simultaneous control for the heat equation with Dirichlet and Neumann boundary conditions JO - Comptes Rendus. Mathématique PY - 2024 SP - 937 EP - 942 VL - 362 IS - G9 PB - Académie des sciences, Paris UR - https://www.numdam.org/articles/10.5802/crmath.535/ DO - 10.5802/crmath.535 LA - en ID - CRMATH_2024__362_G9_937_0 ER -
%0 Journal Article %A Burq, Nicolas %A Moyano, Ivan %T Simultaneous control for the heat equation with Dirichlet and Neumann boundary conditions %J Comptes Rendus. Mathématique %D 2024 %P 937-942 %V 362 %N G9 %I Académie des sciences, Paris %U https://www.numdam.org/articles/10.5802/crmath.535/ %R 10.5802/crmath.535 %G en %F CRMATH_2024__362_G9_937_0
Burq, Nicolas; Moyano, Ivan. Simultaneous control for the heat equation with Dirichlet and Neumann boundary conditions. Comptes Rendus. Mathématique, Tome 362 (2024) no. G9, pp. 937-942. doi: 10.5802/crmath.535
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