# Identification of a wave equation generated by a string

ESAIM: Control, Optimisation and Calculus of Variations (2014)

- Volume: 20, Issue: 4, page 1203-1213
- ISSN: 1292-8119

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topBoumenir, Amin. "Identification of a wave equation generated by a string." ESAIM: Control, Optimisation and Calculus of Variations 20.4 (2014): 1203-1213. <http://eudml.org/doc/272826>.

@article{Boumenir2014,

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.},

author = {Boumenir, Amin},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {inverse spectral methods; Krein string; Gelfand-levitan theory; inverse problem; wave equation; Krein's inverse spectral theory; Gelfand-Levitan theory},

language = {eng},

number = {4},

pages = {1203-1213},

publisher = {EDP-Sciences},

title = {Identification of a wave equation generated by a string},

url = {http://eudml.org/doc/272826},

volume = {20},

year = {2014},

}

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

PB - EDP-Sciences

VL - 20

IS - 4

SP - 1203

EP - 1213

AB - 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.

LA - eng

KW - inverse spectral methods; Krein string; Gelfand-levitan theory; inverse problem; wave equation; Krein's inverse spectral theory; Gelfand-Levitan theory

UR - http://eudml.org/doc/272826

ER -

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