The wave equation with oscillating density: observability at low frequency

Gilles Lebeau

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 5, page 219-258
  • ISSN: 1292-8119

Abstract

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We prove an observability estimate for a wave equation with rapidly oscillating density, in a bounded domain with Dirichlet boundary condition.

How to cite

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Lebeau, Gilles. "The wave equation with oscillating density: observability at low frequency." ESAIM: Control, Optimisation and Calculus of Variations 5 (2010): 219-258. <http://eudml.org/doc/197278>.

@article{Lebeau2010,
abstract = { We prove an observability estimate for a wave equation with rapidly oscillating density, in a bounded domain with Dirichlet boundary condition. },
author = {Lebeau, Gilles},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Bloch wave; observability; microlocal defect measures.; Dirichlet boundary condition; singular perturbation},
language = {eng},
month = {3},
pages = {219-258},
publisher = {EDP Sciences},
title = {The wave equation with oscillating density: observability at low frequency},
url = {http://eudml.org/doc/197278},
volume = {5},
year = {2010},
}

TY - JOUR
AU - Lebeau, Gilles
TI - The wave equation with oscillating density: observability at low frequency
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 5
SP - 219
EP - 258
AB - We prove an observability estimate for a wave equation with rapidly oscillating density, in a bounded domain with Dirichlet boundary condition.
LA - eng
KW - Bloch wave; observability; microlocal defect measures.; Dirichlet boundary condition; singular perturbation
UR - http://eudml.org/doc/197278
ER -

References

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  5. C. Castro, Boundary controllability of the one dimensional wave equation with rapidly oscillating density, preprint.  Zbl0940.93016
  6. C. Castro and E. Zuazua, Contrôle de l'équation des ondes à densité rapidement oscillante à une dimension d'espace. C. R. Acad. Sci. Paris324 (1997) 1237-1242.  
  7. P. Gérard, Mesures semi-classiques et ondes de Bloch, Séminaire X EDP, exposé 16 (1991).  Zbl0739.35096
  8. P. Gérard and E. Leichtnam, Ergodic properties of eigenfunctions for the Dirichlet problem. Duke Math. J.71 (1993) 559-607.  Zbl0788.35103
  9. G. Lebeau, Contrôle de l'équation de Schrödinger. J. Math. Pures Appl.71 (1993) 267-291.  
  10. G. Lebeau, Équation des ondes amorties, Algebraic and Geometric Methods in Mathematical Physics, A. Boutet de Monvel and V. Marchenko, Eds. Kluwer Academic Publishers (1996) 73-109.  Zbl0863.58068
  11. R. Melrose and J. Sjöstrand, Singularities of boundary value problems I, II. Comm. Pure Appl. Math. 31 (1978) 593-617; 35 (1982) 129-168.  Zbl0368.35020

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