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Identification of a wave equation generated by a string∗

Published online by Cambridge University Press:  08 August 2014

Amin Boumenir
Amin Boumenir*
Affiliation:
Department of Mathematics, College of Science, Kuwait. University, P.O. Box 5969, 13060 Safat, Kuwait. boumenir@sci.kuniv.edu.kw

Abstract

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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.

Keywords

Inverse spectral methods; Krein string; Gelfand-Levitan theory

Information

Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 20 , Issue 4 , October 2014, pp. 1203 - 1213
Copyright
© EDP Sciences, SMAI, 2014

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