Decay of solutions of the elastic wave equation with a localized dissipation

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1. [1] Anné ( C.). - A shift between Dirichlet and Neumann spectrum for generalized linear elasticity. Asymptot. Anal.19, 3-4, p. 297-316 (1999). Zbl0943.74005MR1696228
2. [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. [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). Zbl0978.35077MR1799852
4. [4] Bellassoued ( M.). - Carleman Estimates and Distribution of Resonances for the transparent Obstacle and Application to the Stabilization . To appear in Asymptotic analysis. Zbl1137.35388MR2011790
5. [5] Bellassoued ( M.). - Unicité et Contrôle pour le système de Lamé. Optimisation and Calculus of Variations. ESAIM:COCV6, p. 561-592, September 2001. Zbl1007.35006
6. [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). Zbl0918.35081MR1618254
7. [7] Hörmander ( L.). - The analysis of linear partial differential operators, Springer Verlag Tomes 1, 2, 3. 
8. [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). Zbl0913.93062MR1627344
9. [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). Zbl0795.35061MR1177309
10. [10] Lagnese ( J.). - Boundary Stabilization of Linear Elastodynamic systems, SIAM J. Control and Optimization21, 6, p. 968-984 (1983). Zbl0531.93044MR719524
11. [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). Zbl0780.93082MR1142681
12. [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). Zbl0863.58068MR1385677
13. [13] Lebeau ( G. ) and Robbiano ( L.). — Stabilisation de l'equation des ondes par le bord, Duke math. J.86, 3, p. 465-491 (1997). Zbl0884.58093MR1432305
14. [14] Lions ( J.-L. ). - Contrôlabilité exacte, perturbations et stabilisation de systèmes distribués. Tome 1. 8. Masson, Paris, (1988). Zbl0653.93002
15. [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). Zbl0896.35023MR1411157
16. [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). Zbl0432.73021MR535598
17. [17] Taylor ( M. ). - Reflection of singularities of solution to systems of differential equations, Comm. Pure App. Math.28, p. 457-478 (1975). Zbl0332.35058MR509098
18. [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). Zbl0669.73017MR945621
19. [19] Wolka ( J.T. ) , Rowley ( B.), Lawruk ( B.). - Boundary value problems for elliptic systems. Cambridge University Press , Cambridge, (1995). Zbl0836.35042MR1343490

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