no. 3
Decay of solutions of the elastic wave equation with a localized dissipation
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 12 (2003) no. 3, pp. 267-301. 
@article{AFST_2003_6_12_3_267_0,
     author = {Bellassoued, Mourad},
     title = {Decay of solutions of the elastic wave equation with a localized dissipation},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {267--301},
     publisher = {Universit\'e Paul Sabatier, Institut de math\'ematiques},
     address = {Toulouse},
     volume = {Ser. 6, 12},
     number = {3},
     year = {2003},
     mrnumber = {2030088},
     zbl = {1073.35036},
     language = {en},
     url = {http://www.numdam.org/item/AFST_2003_6_12_3_267_0/}
}
TY  - JOUR
AU  - Bellassoued, Mourad
TI  - Decay of solutions of the elastic wave equation with a localized dissipation
JO  - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY  - 2003
SP  - 267
EP  - 301
VL  - 12
IS  - 3
PB  - Université Paul Sabatier, Institut de mathématiques
PP  - Toulouse
UR  - http://www.numdam.org/item/AFST_2003_6_12_3_267_0/
LA  - en
ID  - AFST_2003_6_12_3_267_0
ER  - 
%0 Journal Article
%A Bellassoued, Mourad
%T Decay of solutions of the elastic wave equation with a localized dissipation
%J Annales de la Faculté des sciences de Toulouse : Mathématiques
%D 2003
%P 267-301
%V 12
%N 3
%I Université Paul Sabatier, Institut de mathématiques
%C Toulouse
%U http://www.numdam.org/item/AFST_2003_6_12_3_267_0/
%G en
%F AFST_2003_6_12_3_267_0
Bellassoued, Mourad. Decay of solutions of the elastic wave equation with a localized dissipation. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 12 (2003) no. 3, pp. 267-301. http://www.numdam.org/item/AFST_2003_6_12_3_267_0/

[1] Anné (C.). - A shift between Dirichlet and Neumann spectrum for generalized linear elasticity. Asymptot. Anal. 19, 3-4, p. 297-316 (1999). | MR | Zbl

[2] Bardos (C. ) , Lebeau ( G.) and Rauch (J.). - Contrôle et stabilisation dans les problèmes hyperboliques. Appendix, in Lions, Tome1, Controlabilite exacte, stabilisation et perturbations des systemes distribués, Masson, RMA 8, ( 1988).

[3] Bellassoued ( M.). - Distribution of Resonances and Decay Rate of the Local energy for the Elastic Wave Equation. Comm. Math. Phys. 215, p. 575-408 (2000). | MR | Zbl

[4] Bellassoued ( M.). - Carleman Estimates and Distribution of Resonances for the transparent Obstacle and Application to the Stabilization . To appear in Asymptotic analysis. | MR | Zbl

[5] Bellassoued ( M.). - Unicité et Contrôle pour le système de Lamé. Optimisation and Calculus of Variations. ESAIM:COCV 6, p. 561-592, September 2001. | Numdam | Zbl

[6] Burq (N.). - Décroissance de l'energie locale de l'equation des ondes pour le problème exterieur et absence de résonances au voisinage du réel , Acta Math. 180, 1, p. 1-29 (1998). | MR | Zbl

[7] Hörmander (L.). - The analysis of linear partial differential operators, Springer Verlag Tomes 1, 2, 3.

[8] Horn (A.M. ). - Implications of sharp trace regularity results on boundary stabilization of the system of linear elasticity. J. Math. Anal. Appl. 223, 1, p. 126-150 (1998). | MR | Zbl

[9] Kawashita ( M.). - On the Local Energy Decay Property for the Elastic Wave equation with Neumann boundary condition, Duke Math. J. 67, p. 333-351 (1992). | MR | Zbl

[10] Lagnese ( J.). - Boundary Stabilization of Linear Elastodynamic systems, SIAM J. Control and Optimization 21, 6, p. 968-984 (1983). | MR | Zbl

[11] Lasiecka ( I.) and Triggiani (R.). - Uniform stabilization of the wave equation with Dirichlet or Neumann feedback control without geometrical conditions. Appl. Math. Optim. 25, 2, p. 189-224 (1992). | MR | Zbl

[12] Lebeau (G. ). - Equation des ondes amorties. In A. Boutet de Monvel and V. Marchenko, editors, Algebraic and Geometric Methods in Mathematical Physics. Kluwer Academic, the Netherlands, p. 73-109 (1996). | MR | Zbl

[13] Lebeau (G. ) and Robbiano (L.). - Stabilisation de l'equation des ondes par le bord, Duke math. J. 86, 3, p. 465-491 (1997). | MR | Zbl

[14] Lions (J.-L. ). - Contrôlabilité exacte, perturbations et stabilisation de systèmes distribués. Tome 1. 8. Masson, Paris, (1988). | Zbl

[15] Tataru (D. ). - Carleman estimates and unique continuation for solutions to boundary value problems. J. Math. Pures Appl. (9) 75, 4, p. 367-408 (1996). | MR | Zbl

[16] Taylor (M. ). - Rayleigh waves in linear elasticity as a propagation of singularities phenomenon. Part. Diff. Equat and Geo (Proc. Conf., Park City, Utah, 1977, p. 273-291, Lecture Notes in Pure and Appl. Math , 48, Dekker, New York, (1979). | MR | Zbl

[17] Taylor (M. ). - Reflection of singularities of solution to systems of differential equations, Comm. Pure App. Math. 28, p. 457-478 (1975). | MR | Zbl

[18] Yamamoto ( K.). - Singularities of solutions to the boundary value problems for elastic and Maxwell's equations, Japan. J. Math. 14, 1, p. 119-163 (1988). | MR | Zbl

[19] Wolka (J.T. ) , Rowley ( B.), Lawruk (B.). - Boundary value problems for elliptic systems. Cambridge University Press , Cambridge, (1995). | MR | Zbl