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.
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.
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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 = {https://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 - https://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 https://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, Volume 342 (2006) no. 8, pp. 579-584. doi : 10.1016/j.crma.2006.02.023. https://www.numdam.org/articles/10.1016/j.crma.2006.02.023/
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