The wave equation with oscillating density : observability at low frequency

Gilles Lebeau

ESAIM: Control, Optimisation and Calculus of Variations (2000)

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

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Lebeau, Gilles. "The wave equation with oscillating density : observability at low frequency." ESAIM: Control, Optimisation and Calculus of Variations 5 (2000): 219-258. <http://eudml.org/doc/90569>.

@article{Lebeau2000,
author = {Lebeau, Gilles},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Dirichlet boundary condition; singular perturbation},
language = {eng},
pages = {219-258},
publisher = {EDP Sciences},
title = {The wave equation with oscillating density : observability at low frequency},
url = {http://eudml.org/doc/90569},
volume = {5},
year = {2000},
}

TY - JOUR
AU - Lebeau, Gilles
TI - The wave equation with oscillating density : observability at low frequency
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2000
PB - EDP Sciences
VL - 5
SP - 219
EP - 258
LA - eng
KW - Dirichlet boundary condition; singular perturbation
UR - http://eudml.org/doc/90569
ER -

References

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  1. [1] M. Avellaneda, C. Bardos and J. Rauch, Contrôlabilité exacte, homogénéisation et localisation d'ondes dans un milieu non-homogène. Asymptot. Anal. 5 ( 1992) 481-484. Zbl0763.93006MR1169354
  2. [2] G. Allaire and C. Conca, Bloch wave homogenization and spectral asymptotic analysis. J. Math. Pures Appl. 77 ( 1998) 153-208. Zbl0901.35005MR1614641
  3. [3] N. Burq and G. Lebeau, Mesures de défaut de compacité; applications au système de Lamé, preprint. MR1872422
  4. [4] C. Bardos, G. Lebeau and J. Rauch, Sharp sufficient conditions for the observation, control and stabilization of waves from the boundary. SIAM J. Control Optim. 30 ( 1992) 1024-1075. Zbl0786.93009MR1178650
  5. [5] C. Castro, Boundary controllability of the one dimensional wave equation with rapidly oscillating density, preprint. Zbl0940.93016MR1715339
  6. [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. Paris 324 ( 1997) 1237-1242. Zbl1007.93036MR1456294
  7. [7] P. Gérard, Mesures semi-classiques et ondes de Bloch, Séminaire X EDP, exposé 16 ( 1991). Zbl0739.35096MR1131589
  8. [8] P. Gérard and E. Leichtnam, Ergodic properties of eigenfunctions for the Dirichlet problem. Duke Math. J. 71 ( 1993) 559-607. Zbl0788.35103MR1233448
  9. [9] G. Lebeau, Contrôle de l'équation de SchrödingerJ. Math. Pures Appl. 71 ( 1993) 267-291. Zbl0838.35013MR1172452
  10. [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. Zbl0863.58068MR1385677
  11. [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. Zbl0546.35083MR492794

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