Dans cette Note, nous considérons la contrôlabilité asymptotique et la contrôlabilité nulle asymptotique pour des systèmes hyperboliques linéaires en dimension dʼespace un. Nous établissons quʼelles sont équivalentes, respectivement, à lʼobservabilité forte et lʼobservabilité faible du système dual. Nous donnons un exemple dʼun système hyperbolique sousmis à un seul contrôle frontière, qui est asymptotiquement contrôlable mais non exactement contrôlable.
In this Note we introduce the asymptotic controllability and the asymptotic null controllability for 1-D linear hyperbolic systems under the lack of boundary controls. We claim that they are equivalent, respectively, to the strong observability and the weak observability for the dual system. An example of hyperbolic system with only one boundary control is shown to be asymptotically controllable but not exactly controllable.
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@article{CRMATH_2011__349_11-12_663_0,
author = {Li, Tatsien and Rao, Bopeng},
title = {Contr\^olabilit\'e asymptotique de syst\`emes hyperboliques lin\'eaires},
journal = {Comptes Rendus. Math\'ematique},
pages = {663--668},
publisher = {Elsevier},
volume = {349},
number = {11-12},
year = {2011},
doi = {10.1016/j.crma.2011.03.006},
language = {fr},
url = {http://www.numdam.org/articles/10.1016/j.crma.2011.03.006/}
}
TY - JOUR AU - Li, Tatsien AU - Rao, Bopeng TI - Contrôlabilité asymptotique de systèmes hyperboliques linéaires JO - Comptes Rendus. Mathématique PY - 2011 SP - 663 EP - 668 VL - 349 IS - 11-12 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2011.03.006/ DO - 10.1016/j.crma.2011.03.006 LA - fr ID - CRMATH_2011__349_11-12_663_0 ER -
%0 Journal Article %A Li, Tatsien %A Rao, Bopeng %T Contrôlabilité asymptotique de systèmes hyperboliques linéaires %J Comptes Rendus. Mathématique %D 2011 %P 663-668 %V 349 %N 11-12 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2011.03.006/ %R 10.1016/j.crma.2011.03.006 %G fr %F CRMATH_2011__349_11-12_663_0
Li, Tatsien; Rao, Bopeng. Contrôlabilité asymptotique de systèmes hyperboliques linéaires. Comptes Rendus. Mathématique, Tome 349 (2011) no. 11-12, pp. 663-668. doi : 10.1016/j.crma.2011.03.006. http://www.numdam.org/articles/10.1016/j.crma.2011.03.006/
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