Geodesic
Identification of a wave equation generated by a string
ESAIM: Control, Optimisation and Calculus of Variations, Tome 20 (2014) no. 4, pp. 1203-1213

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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.

DOI : 10.1051/cocv/2014012
Classification : 34A55, 34K29, 34L05
Keywords: inverse spectral methods, Krein string, Gelfand-levitan theory 
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     author = {Boumenir, Amin},
     title = {Identification of a wave equation generated by a string},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {1203--1213},
     publisher = {EDP-Sciences},
     volume = {20},
     number = {4},
     year = {2014},
     doi = {10.1051/cocv/2014012},
     mrnumber = {3264239},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2014012/}
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Boumenir, Amin. Identification of a wave equation generated by a string. ESAIM: Control, Optimisation and Calculus of Variations, Tome 20 (2014) no. 4, pp. 1203-1213. doi: 10.1051/cocv/2014012

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