[Contrôlabilité exacte dʼun système en cascade dʼéquations conservatives]
On considère un système en cascade de deux équations conservatives et lʼon prouve la contrôlabilité du système complet lorsque chaque équation est contrôlable et que le groupe unitaire correspondant à lʼévolution libre est périodique en temps. Ce résultat sʼapplique à des systèmes dʼéquations de Schrödinger ou des ondes. Utilisant la transformée de Kannai, on en déduit quʼun système en cascade dʼéquations de la chaleur est contrôlable à zéro en dimension un, même si les supports du contrôle et du couplage ne sʼintersectent pas.
We consider a cascade system of two conservative equations and prove the controllability of the full system when each equation is controllable, provided that the unitary group corresponding to the free evolution is time-periodic. Applications to systems of Schrödinger (resp. wave) equations are given. With the aid of Kannai transform we infer that a one-dimensional system of heat equations is null controllable even if the supports of the control function and of the coupling term do not intersect.
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@article{CRMATH_2011__349_5-6_291_0,
author = {Rosier, Lionel and de Teresa, Luz},
title = {Exact controllability of a cascade system of conservative equations},
journal = {Comptes Rendus. Math\'ematique},
pages = {291--296},
publisher = {Elsevier},
volume = {349},
number = {5-6},
year = {2011},
doi = {10.1016/j.crma.2011.01.014},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2011.01.014/}
}
TY - JOUR AU - Rosier, Lionel AU - de Teresa, Luz TI - Exact controllability of a cascade system of conservative equations JO - Comptes Rendus. Mathématique PY - 2011 SP - 291 EP - 296 VL - 349 IS - 5-6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2011.01.014/ DO - 10.1016/j.crma.2011.01.014 LA - en ID - CRMATH_2011__349_5-6_291_0 ER -
%0 Journal Article %A Rosier, Lionel %A de Teresa, Luz %T Exact controllability of a cascade system of conservative equations %J Comptes Rendus. Mathématique %D 2011 %P 291-296 %V 349 %N 5-6 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2011.01.014/ %R 10.1016/j.crma.2011.01.014 %G en %F CRMATH_2011__349_5-6_291_0
Rosier, Lionel; de Teresa, Luz. Exact controllability of a cascade system of conservative equations. Comptes Rendus. Mathématique, Tome 349 (2011) no. 5-6, pp. 291-296. doi : 10.1016/j.crma.2011.01.014. http://www.numdam.org/articles/10.1016/j.crma.2011.01.014/
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