Identification of a wave equation generated by a string

Amin Boumenir

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

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

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.

How to cite

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Boumenir, 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 -

References

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