The wave equation with oscillating density: Observability at low frequency

ESAIM - Control, Optimisation and Calculus of Variations

Volumn 5, Issue , 2000, Pages 219-258

  Lebeau, Gilles ^a  

^a ECOLE POLYTECHNIQUE   (France)

Author keywords

Bloch wave; Microlocal defect measures; Observability

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; FOURIER TRANSFORMS; INTEGRAL EQUATIONS; LAPLACE TRANSFORMS; MATRIX ALGEBRA; PERTURBATION TECHNIQUES; SPECTRUM ANALYSIS; THEOREM PROVING; WAVE EQUATIONS;

BLOCH WAVE; DIRICHLET BOUNDARY CONDITION; MICROLOCAL DEFECT MEASURE; OSCILLATING DENSITY; SMOOTH BOUNDED DOMAIN;

OBSERVABILITY;

EID: 0034425469     PISSN: 12928119     EISSN: 12623377     Source Type: Journal    
DOI: 10.1051/cocv:2000109     Document Type: Article

References (11)

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.
2. G. Allaire and C. Conca, Bloch wave homogenization and spectral asymptotic analysis. J. Math. Pures Appl. 77 (1998) 153-208.
3. N. Burq and G. Lebeau, Mesures de defaut de compacite; applications au systeme de Lame, preprint.
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.
5. C. Castro, Boundary controllability of the one dimensional wave equation with rapidly oscillating density, preprint.
6. C. Castro and E. Zuazua, Contrôle de l’equation des ondes à densite rapidement oscillante a une dimension d’espace. C. R. Acad. Sci. Paris 324 (1997) 1237-1242.
7. P. Gerard, Mesures semi-classiques et ondes de Bloch, Seminaire X EDP, expose 16 (1991).
8. P. Gerard and E. Leichtnam, Ergodic properties of eigenfunctions for the Dirichlet problem. Duke Math. J. 71 (1993) 559-607.
9. G. Lebeau, Controle de l’equation de Schrodinger. J. Math. Pures Appl. 71 (1993) 267-291.
10. G. Lebeau, Equation des ondes amorties, Algebraic and Geometric Methods in Mathematical Physics, A. Boutet de Monvel and V. Marchenko, Eds. Kluwer Academic Publishers (1996) 73-109.
11. R. Melrose and J. Sjostrand, Singularities of boundary value problems I, II. Comm. Pure Appl. Math. 31 (1978) 593-617; 35 (1982) 129-168.