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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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Volume 19, Issue 3 (Jan 2011)

Issues

Exponential instability in the Gel'fand inverse problem on the energy intervals

Mikhail Ismailovitch Isaev
  • Moscow Institute of Physics and Technology, 141700 Dolgoprudny, Russia.
  • Centre de Mathématiques Appliquées, Ecole Polytechnique, 91128 Palaiseau, France.
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Published Online: 2011-08-05 | DOI: https://doi.org/10.1515/jiip.2011.039

Abstract

We consider the Gel'fand inverse problem and continue studies of Mandache (Inverse Problems 17: 1435–1444, 2001). We show that the Mandache-type instability remains valid even in the case of Dirichlet-to-Neumann map given on the energy intervals. These instability results show, in particular, that the logarithmic stability estimates of Alessandrini (Appl. Anal. 27: 153–172, 1988), Novikov and Santacesaria (J. Inverse Ill-Posed Probl., 2010) and especially of Novikov (2010) are optimal (up to the value of the exponent).

Keywords.: Hyperbolic equations; Gel'fand inverse problem; Dirichlet-to-Neumann map; stability and instability estimates

About the article

Received: 2011-01-03

Published Online: 2011-08-05

Published in Print: 2011-08-01


Citation Information: Journal of Inverse and Ill-posed Problems, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip.2011.039.

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[1]
Anupam Pal Choudhury and Horst Heck
Mathematical Methods in the Applied Sciences, 2017
[2]
M I Isaev and R G Novikov
Inverse Problems, 2014, Volume 30, Number 9, Page 095006
[3]
Михаил Исмаилович Исаев and Mikhail Ismailovich Isaev
Функциональный анализ и его приложения, 2013, Volume 47, Number 3, Page 28
[4]
M. I. Isaev
Functional Analysis and Its Applications, 2013, Volume 47, Number 3, Page 187
[5]
M.I. Isaev
Applicable Analysis, 2013, Volume 92, Number 11, Page 2262
[7]
Matteo Santacesaria
Bulletin des Sciences Mathématiques, 2012, Volume 136, Number 7, Page 731

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