Comptes Rendus
no. 21-22
Partial Differential Equations/Optimal Control
Observability estimate for stochastic Schrödinger equations
[Inégalité d'observabilité pour les équations de Schrödinger stochastiques]

Présenté par : Alain Bensousson

Qi Lü1, 2
1 School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 610054, China
2 School of Mathematics, Sichuan University, Chengdu 610064, China
Comptes Rendus. Mathématique, Volume 348 (2010) no. 21-22, pp. 1159-1162.

Dans cette Note, nous établissons une inégalité d'observabilité pour les équations de Schrödinger stochastiques avec des termes d'ordre inférieur à coefficients non réguliers. Notre inégalité s'obtient à partir des inégalités de Carleman globales qui découlent d'une identité à poids pour les opérateurs de type Schrödinger stochastiques. Comme conséquence intéressante de cette identité, on retrouve tous les résultats connus de controlabilité/observabilité pour les équations aux dérivées partielles stochastiques et déterministes, de type Schrödinger et hyperboliques, où l'utilisation des inégalités de Carleman a joué un rôle.

In this Note, we present an observability estimate for stochastic Schrödinger equations with nonsmooth lower order terms. The desired inequality is derived by a global Carleman estimate which is based on a fundamental weighted identity for stochastic Schrödinger-like operator. As an interesting byproduct, starting from this identity, one can deduce all the known controllability/observability results for several stochastic and deterministic partial differential equations that are derived before via Carleman estimate in the literature.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.10.016
Qi Lü 1, 2

1 School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 610054, China
2 School of Mathematics, Sichuan University, Chengdu 610064, China 
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     title = {Observability estimate for stochastic {Schr\"odinger} equations},
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     pages = {1159--1162},
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     doi = {10.1016/j.crma.2010.10.016},
     language = {en},
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Qi Lü. Observability estimate for stochastic Schrödinger equations. Comptes Rendus. Mathématique, Volume 348 (2010) no. 21-22, pp. 1159-1162. doi : 10.1016/j.crma.2010.10.016. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.10.016/

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