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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


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Rank 59 out of 312 in category Mathematics and 93 out of 254 in Applied Mathematics in the 2015 Thomson Reuters Journal Citation Report/Science Edition

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Source Normalized Impact per Paper (SNIP) 2015: 1.106
Impact per Publication (IPP) 2015: 0.712

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1569-3945
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Determining the potential in the Schrödinger equation from the Dirichlet to Neumann map by the boundary control method

S. Avdonin / S. Lenhart / V. Protopopescu

Department of Mathematical Sciences, University of Alaska, Fairbanks, AK 99775-6660. E-mail:

Department of Mathematics, University of Tennessee, Knoxville, TN 37996–1300

Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831–6016

Citation Information: Journal of Inverse and Ill-posed Problems jiip. Volume 13, Issue 4, Pages 317–330, ISSN (Online) 1569-3953, ISSN (Print) 0928-0219, DOI: 10.1515/156939405775201718,

Publication History

Published Online:

We consider the problem of identifying the potential in the one-dimensional Schrödinger equation with input Dirichlet data, from measured Neumann data. Knowledge of the Dirichlet to Neumann map together with spectral controllability results for the Schrödinger equation obtained using properties of exponential Riesz bases allow recovery of the spectral data. Once the the spectral data is recovered, we use the Boundary Control method to solve the identification problem.

Citing Articles

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[1]
S. A. Avdonin and V. S. Mikhaylov
Journal of Mathematical Sciences, 2012, Volume 185, Number 4, Page 513
[2]
Sergei Avdonin and Jonathan Bell
Journal of Mathematical Biology, 2013, Volume 67, Number 1, Page 123
[3]
Mourad Bellassoued and Mourad Choulli
Journal of Functional Analysis, 2010, Volume 258, Number 1, Page 161
[4]
Amin Boumenir and Vu Kim Tuan
Inverse Problems and Imaging, 2011, Volume 5, Number 4, Page 775
[5]
Vu Tuan
Fractional Calculus and Applied Analysis, 2011, Volume 14, Number 1
[6]
Mourad Bellassoued and David Dos Santos Ferreira
Inverse Problems, 2010, Volume 26, Number 12, Page 125010
[7]
Sergei Avdonin and Victor Mikhaylov
Inverse Problems, 2010, Volume 26, Number 4, Page 045009
[8]
M I Belishev
Inverse Problems, 2007, Volume 23, Number 5, Page R1

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