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

@article{COCV_2014__20_4_1203_0, 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://archive.numdam.org/articles/10.1051/cocv/2014012/} }

TY - JOUR AU - Boumenir, Amin TI - Identification of a wave equation generated by a string JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2014 SP - 1203 EP - 1213 VL - 20 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2014012/ DO - 10.1051/cocv/2014012 LA - en ID - COCV_2014__20_4_1203_0 ER -

%0 Journal Article %A Boumenir, Amin %T Identification of a wave equation generated by a string %J ESAIM: Control, Optimisation and Calculus of Variations %D 2014 %P 1203-1213 %V 20 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2014012/ %R 10.1051/cocv/2014012 %G en %F COCV_2014__20_4_1203_0

Boumenir, Amin. Identification of a wave equation generated by a string. ESAIM: Control, Optimisation and Calculus of Variations, Volume 20 (2014) no. 4, pp. 1203-1213. doi : 10.1051/cocv/2014012. http://archive.numdam.org/articles/10.1051/cocv/2014012/

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