Inverse problem for the Schrödinger operator in an unbounded strip

Cardoulis, Laure; Cristofol, Michel; Gaitan, Patricia

doi:10.1016/j.crma.2008.04.004

Partial Differential Equations

Inverse problem for the Schrödinger operator in an unbounded strip
[Un problème inverse pour l'opérateur de Schrödinger dans une bande]

Présenté par : Gilles Lebeau

Cardoulis, Laure ¹ ; Cristofol, Michel ² ; Gaitan, Patricia ²

¹ CEREMATH/UMR MIP, Université de Toulouse 1, 21, allées de Brienne, 31000 Toulouse, France
² Laboratoire d'Analyse Topologie Probabilités, CNRS UMR 6632, Universités d'Aix-Marseille, 13453 Marseille cedex, France

Comptes Rendus. Mathématique, Tome 346 (2008) no. 11-12, pp. 635-640.

Résumé
Abstract

Nous démontrons une estimation globale de Carleman et une estimation d'énergie pour l'opérateur de Schrödinger $H : = i \partial_{t} + \nabla \cdot (c \nabla)$ dans une bande non bornée. Ces estimations nous permettent de donner un résultat de stabilité pour le coefficient de diffusion $c (x, y)$ à partir de la mesure de la dérivée normale de la solution sur une partie du bord.

We prove an adapted global Carleman estimate and an energy estimate for the Schrödinger operator $H : = i \partial_{t} + \nabla \cdot (c \nabla)$ in an unbounded strip. Using these estimates, we give a stability result for the diffusion coefficient $c (x, y)$ from the measurement of the normal derivative of the solution on a part of the boundary.

Reçu le : 2007-05-24
Accepté le : 2008-04-11
Publié le : 2008-04-29

DOI : 10.1016/j.crma.2008.04.004

Affiliations des auteurs :

Cardoulis, Laure ¹ ; Cristofol, Michel ² ; Gaitan, Patricia ²

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     title = {Inverse problem for the {Schr\"odinger} operator in an unbounded strip},
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     pages = {635--640},
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Cardoulis, Laure; Cristofol, Michel; Gaitan, Patricia. Inverse problem for the Schrödinger operator in an unbounded strip. Comptes Rendus. Mathématique, Tome 346 (2008) no. 11-12, pp. 635-640. doi : 10.1016/j.crma.2008.04.004. http://www.numdam.org/articles/10.1016/j.crma.2008.04.004/

Bibliographie
Cité par

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