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Identification of a wave equation generated by a string

Published online by Cambridge University Press:  08 August 2014

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

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.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2014

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