| Issue |
ESAIM: COCV
Volume 20, Number 4, October-December 2014
|
|
|---|---|---|
| Page(s) | 1203 - 1213 | |
| DOI | https://doi.org/10.1051/cocv/2014012 | |
| Published online | 08 August 2014 | |
Identification of a wave equation generated by a string∗
Department of Mathematics, College of Science, Kuwait.
University, P.O. Box
5969, 13060
Safat,
Kuwait
boumenir@sci.kuniv.edu.kw
Received: 27 June 2013
Revised: 5 November 2013
We show that we can reconstruct two coefficients of a wave equation by a single boundary measurement of the solution. The identification and reconstruction are based on Krein’s inverse spectral theory for the first coefficient and on the Gelfand−Levitan theory for the second. To do so we use spectral estimation to extract the first spectrum and then interpolation to map the second one. The control of the solution is also studied.
Mathematics Subject Classification: 34A55 / 34K29 / 34L05
Key words: Inverse spectral methods; Krein string; Gelfand-Levitan theory
© EDP Sciences, SMAI, 2014
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