Comptes Rendus
no. 19-20
Partial Differential Equations
An inverse problem for a time-dependent Schrödinger operator in an unbounded strip
[Un problème inverse pour un opérateur de Schrödinger dépendant du temps dans une bande non bornée]

Présenté par : the Editorial Board

Laure Cardoulis1, 2
1 Université de Toulouse, UT1 Ceremath, 21 Allées de Brienne, 31042 Toulouse cedex, France
2 Institut de Mathématiques de Toulouse UMR 5219, 31042 Toulouse cedex, France
Comptes Rendus. Mathématique, Volume 350 (2012) no. 19-20, pp. 891-896.

Dans cette Note, on prouve un résultat de stabilité pour deux coefficients indépendants (chacun dʼeux dépendant dʼune seule variable dʼespace et le potentiel dépendant aussi de la variable temps) pour un opérateur de Schrödinger avec une observation sur une partie non bornée du bord et la donnée de la solution à un temps fixé sur tout le domaine.

In this Note we prove a stability result for two independent coefficients (each one depending on only one space variable and the potential also depending on the time variable) for a time-dependent Schrödinger operator in an unbounded strip with one observation on an unbounded subset of the boundary and the data of the solution at a fixed time on the whole domain.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2012.10.006
Laure Cardoulis 1, 2

1 Université de Toulouse, UT1 Ceremath, 21 Allées de Brienne, 31042 Toulouse cedex, France
2 Institut de Mathématiques de Toulouse UMR 5219, 31042 Toulouse cedex, France 
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Laure Cardoulis. An inverse problem for a time-dependent Schrödinger operator in an unbounded strip. Comptes Rendus. Mathématique, Volume 350 (2012) no. 19-20, pp. 891-896. doi : 10.1016/j.crma.2012.10.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.10.006/

[1] L. Baudouin; J.P. Puel Uniqueness and stability in an inverse problem for the Schrödinger equation, Inverse Problems, Volume 18 (2002), pp. 1537-1554

[2] L. Cardoulis; M. Cristofol; P. Gaitan Inverse problem for the Schrödinger operator in an unbounded strip, J. Inverse and Ill-Posed Problems, Volume 16 (2008) no. 2, pp. 127-146

[3] L. Cardoulis; P. Gaitan Identification of two independent coefficients with one observation for the Schrödinger operator in an unbounded strip, C. R. Acad. Sci. Paris, Ser. I, Volume 348 (2010), pp. 149-153

[4] L. Cardoulis; P. Gaitan Simultaneous identification of the diffusion coefficient and the potential for the Schrödinger operator with only one observation, Inverse Problems, Volume 26 (2010), p. 035012

[5] M. Cristofol; E. Soccorsi Stability estimate in an inverse problem for non autonomous magnetic Schrödinger equations, Applicable Analysis, Volume 90 (2011) no. 10, pp. 1499-1520

[6] O.Yu. Immanuvilov; M. Yamamoto Carleman estimates for the non-stationary Lamé system and the application to an inverse problem, ESAIM Control Optim. Calc. Var., Volume 11 (2005) no. 1, pp. 1-56

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