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Determining the potential in a wave equation without a geometric condition. Extension to the heat equation

Authors: Kaïs Ammari, Mourad Choulli and Faouzi Triki
Journal: Proc. Amer. Math. Soc. 144 (2016), 4381-4392
MSC (2010): Primary 35R30
Published electronically: April 20, 2016
MathSciNet review: 3531187
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Abstract: We prove a logarithmic stability estimate for the inverse problem of determining the potential in a wave equation from boundary measurements obtained by varying the first component of the initial condition. The novelty of the present work is that no geometric condition is imposed to the sub-boundary where the measurements are made. Our results improve those obtained by the first and second authors in an earlier work. We also show how the analysis for the wave equation can be adapted to an inverse coefficient problem for the heat equation.

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Additional Information

Kaïs Ammari
Affiliation: UR Analysis and Control of Pde, UR 13ES64, Department of Mathematics, Faculty of Sciences of Monastir, University of Monastir, 5019 Monastir, Tunisia

Mourad Choulli
Affiliation: Institut Élie Cartan de Lorraine, UMR CNRS 7502, Université de Lorraine, Boulevard des Aiguillettes, BP 70239, 54506 Vandoeuvre les Nancy cedex - Ile du Saulcy, 57045 Metz cedex 01, France

Faouzi Triki
Affiliation: Laboratoire Jean Kuntzmann, UMR CNRS 5224, Université de Joseph Fourier, 38041 Grenoble Cedex 9, France

Keywords: Inverse problem, wave equation, potential, boundary measurements
Received by editor(s): September 28, 2015
Received by editor(s) in revised form: December 19, 2015
Published electronically: April 20, 2016
Additional Notes: The third author was partially supported by Labex PERSYVAL-Lab (ANR-11-LABX-0025-01)
Communicated by: Joachim Krieger
Article copyright: © Copyright 2016 American Mathematical Society

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