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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


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1569-3945
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Inverse problem for the Schrödinger operator in an unbounded strip

L. Cardoulis1 / M. Cristofol2 / P. Gaitan3

1Université de Toulouse 1, UMR 5640, Ceremath/MIP, Place Anatole, France, 31000 Toulouse, France. Email: laure.cardoulis@univ-tlse1.fr

2Université de Provence, CMI, UMR CNRS 6632, 39, rue Joliot Curie, 13453 Marseille Cedex 13, France, Université Paul Cézanne, IUT de Marseille, France. Email: cristo@cmi.univ-mrs.fr

3Université de Provence, CMI, UMR CNRS 6632, 39, rue Joliot Curie, 13453 Marseille Cedex 13, France, Université de la Méditerranée, IUT d'Aix en Provence, France. Email: gaitan@cmi.univ-mrs.fr

Citation Information: Journal of Inverse and Ill-posed Problems. Volume 16, Issue 2, Pages 127–146, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: 10.1515/JIIP.2008.009, May 2008

Publication History

Received:
2007-01-25
:
2007-07-05
Published Online:
2008-05-09

Abstract

We consider the operator H := i∂t + ∇ . (c∇) in an unbounded strip Ω in ℝ2, where . We prove an adapted global Carleman estimate and an energy estimate for this operator. Using these estimates, we give a stability result for the diffusion coefficient c(x, y).

Key words.: Inverse problem; Schrödinger operator; Carleman estimate

Citing Articles

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[1]
Laure Cardoulis
Comptes Rendus Mathematique, 2012, Volume 350, Number 19-20, Page 891
[2]
Chuang Zheng
Mathematical Control and Related Fields, 2015, Volume 5, Number 1, Page 177
[3]
Yavar Kian, Quang Sang Phan, and Eric Soccorsi
Inverse Problems, 2014, Volume 30, Number 5, Page 055016
[5]
Laure Cardoulis and Patricia Gaitan
Comptes Rendus Mathematique, 2010, Volume 348, Number 3-4, Page 149
[6]
Michel Cristofol and Lionel Roques
Mathematical Biosciences, 2008, Volume 215, Number 2, Page 158
[7]
Liviu I Ignat, Ademir F Pazoto, and Lionel Rosier
Inverse Problems, 2012, Volume 28, Number 1, Page 015011
[8]
Michel Cristofol and Eric Soccorsi
Applicable Analysis, 2011, Volume 90, Number 10, Page 1499
[9]
N. Baranibalan, K. Sakthivel, K. Balachandran, and J.-H. Kim
Applicable Analysis, 2009, Volume 88, Number 4, Page 529
[10]
K. Sakthivel, N. Baranibalan, J.-H. Kim, and K. Balachandran
Acta Applicandae Mathematicae, 2010, Volume 111, Number 2, Page 129

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