[Un autre regard sur le coût de contrôle des systèmes d’évolutions linéaires, avec une attention particulière sur les données localisées]
Nous revisitons la question classique du coût de contrôle/d’observation des systèmes d’évolutions linéaires du premier ordre, en commençant par le cas des EDOs, avant de d’étendre l’analyse aux EDPs d’évolution, du premier ordre, en plusieurs dimensions d’espace. Notre analyse couvre le cas des systèmes hyperboliques et des systèmes pseudo-différentiels, notamment ceux obtenus par linéarisation en mécanique des fluides. En particulier, nous examinons le coût de contrôle de données initiales localisées et, dans le cas dispersif, de données initiales semi-classiquement micro-localisées.
We revisit the classical issue of the controllability/observability cost of linear first order evolution systems, starting with ODEs, before turning to some linear first order evolution PDEs in several space dimensions, including hyperbolic systems and pseudo-differential systems obtained by linearization in fluid mechanics. In particular we investigate the cost for localized initial data and, in the dispersive case, for initial data which are semiclassically microlocalized.
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Roberta Bianchini 1 ; Vincent Laheurte 2 ; Frank Sueur 3
CC-BY 4.0
@article{CRMATH_2025__363_G3_241_0,
author = {Roberta Bianchini and Vincent Laheurte and Frank Sueur},
title = {A new look at the controllability cost of linear evolution systems with a long gaze at localized data},
journal = {Comptes Rendus. Math\'ematique},
pages = {241--266},
publisher = {Acad\'emie des sciences, Paris},
volume = {363},
year = {2025},
doi = {10.5802/crmath.725},
language = {en},
}
TY - JOUR AU - Roberta Bianchini AU - Vincent Laheurte AU - Frank Sueur TI - A new look at the controllability cost of linear evolution systems with a long gaze at localized data JO - Comptes Rendus. Mathématique PY - 2025 SP - 241 EP - 266 VL - 363 PB - Académie des sciences, Paris DO - 10.5802/crmath.725 LA - en ID - CRMATH_2025__363_G3_241_0 ER -
%0 Journal Article %A Roberta Bianchini %A Vincent Laheurte %A Frank Sueur %T A new look at the controllability cost of linear evolution systems with a long gaze at localized data %J Comptes Rendus. Mathématique %D 2025 %P 241-266 %V 363 %I Académie des sciences, Paris %R 10.5802/crmath.725 %G en %F CRMATH_2025__363_G3_241_0
Roberta Bianchini; Vincent Laheurte; Frank Sueur. A new look at the controllability cost of linear evolution systems with a long gaze at localized data. Comptes Rendus. Mathématique, Volume 363 (2025), pp. 241-266. doi : 10.5802/crmath.725. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.725/
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