[Une identité avec poids pour des opérateurs aux dérivées partielles du second ordre et ses applications]
Dans cette Note, nous établissons une identité avec poids pour des opérateurs aux dérivées partielles du second ordre. De cette égalité, découlent tous les resultats connus de contrôlabilité/observabilité pour les équations paraboliques, les équations hyperboliques, l'équation de Schrödinger et celle des plaques, tous obtenus à partir des inégalités de Carleman. Par ailleurs, un nouveau résultat de contrôlabilité/observabilité est obtenu pour les équations de type paraboliques avec des coefficients à valeur complexe.
In this Note, a weighted identity for partial differential operators of second order is established. As its applications, one may deduce all the known controllability/observability results for the parabolic, hyperbolic, Schrödinger and plate equations that are derived via Carleman estimate. Meanwhile, a new controllability/observability result is presented for the parabolic equations with a complex principal part.
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@article{CRMATH_2006__342_8_579_0,
author = {Fu, Xiaoyu},
title = {A weighted identity for partial differential operators of second order and its applications},
journal = {Comptes Rendus. Math\'ematique},
pages = {579--584},
publisher = {Elsevier},
volume = {342},
number = {8},
year = {2006},
doi = {10.1016/j.crma.2006.02.023},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2006.02.023/}
}
TY - JOUR AU - Fu, Xiaoyu TI - A weighted identity for partial differential operators of second order and its applications JO - Comptes Rendus. Mathématique PY - 2006 SP - 579 EP - 584 VL - 342 IS - 8 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2006.02.023/ DO - 10.1016/j.crma.2006.02.023 LA - en ID - CRMATH_2006__342_8_579_0 ER -
%0 Journal Article %A Fu, Xiaoyu %T A weighted identity for partial differential operators of second order and its applications %J Comptes Rendus. Mathématique %D 2006 %P 579-584 %V 342 %N 8 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2006.02.023/ %R 10.1016/j.crma.2006.02.023 %G en %F CRMATH_2006__342_8_579_0
Fu, Xiaoyu. A weighted identity for partial differential operators of second order and its applications. Comptes Rendus. Mathématique, Tome 342 (2006) no. 8, pp. 579-584. doi : 10.1016/j.crma.2006.02.023. http://www.numdam.org/articles/10.1016/j.crma.2006.02.023/
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