Stabilization of second order evolution equations by a class of unbounded feedbacks

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1. K. Ammari and M. Tucsnak, Stabilization of Bernoulli-Euler beams by means of a pointwise feedback force. SIAM. J. Control Optim.39 (2000) 1160-1181.  
2. K. Ammari, A. Henrot and M. Tucsnak, Optimal location of the actuator for the pointwise stabilization of a string. C. R. Acad. Sci. Paris Sér. I Math.330 (2000) 275-280.  
3. A. Bamberger, J. Rauch and M. Taylor, A model for harmonics on stringed instruments. Arch. Rational Mech. Anal.79 (1982) 267-290.  
4. C. Bardos, L. Halpern, G. Lebeau, J. Rauch and E. Zuazua, Stabilisation de l'équation des ondes au moyen d'un feedback portant sur la condition aux limites de Dirichlet. Asymptot. Anal.4 (1991) 285-291.  
5. 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) 1024-1065.  
6. A. Bensoussan, G. Da Prato, M.C. Delfour and S.K. Mitter, Representation and control of infinite Dimensional Systems, Vol. I. Birkhauser (1992).  
7. J.W.S. Cassals, An introduction to Diophantine Approximation. Cambridge University Press, Cambridge (1966).  
8. G. Doetsch, Introduction to the theory and application of the Laplace transformation. Springer, Berlin (1974).  
9. A. Haraux, Une remarque sur la stabilisation de certains systèmes du deuxième ordre en temps. Portugal Math.46 (1989) 245-258.  
10. A.E. Ingham, Some trigonometrical inequalities with applications in the theory of series. Math. Z.41 (1936) 367-369.  
11. S. Jaffard, M. Tucsnak and E. Zuazua, Singular internal stabilization of the wave equation. J. Differential Equations145 (1998) 184-215.  
12. V. Komornik, Rapid boundary stabilization of linear distributed systems. SIAM J. Control Optim.35 (1997) 1591-1613.  
13. V. Komornik and E. Zuazua, A direct method for the boundary stabilization of the wave equation. J. Math. Pures Appl.69 (1990) 33-54.  
14. J. Lagnese, Boundary stabilization of thin plates. Philadelphia, SIAM Stud. Appl. Math. (1989).  
15. S. Lang, Introduction to diophantine approximations. Addison Wesley, New York (1966).  
16. J.L. Lions, Contrôlabilité exacte des systèmes distribués. Masson, Paris (1998).  
17. J.L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications, Vol. 1. Dunod, Paris (1968).  
18. F.W.J. Olver, Asymptotic and Special Functions. Academic Press, New York.  
19. A. Pazy, Semigroups of linear operators and applications to partial differential equations. Springer, New York (1983).  
20. R. Rebarber, Exponential stability of beams with dissipative joints: A frequency approach. SIAM J. Control Optim.33 (1995) 1-28.  
21. L. Robbiano, Fonction de coût et contrôle des solutions des équations hyperboliques. Asymptot. Anal.10 (1995) 95-115.  
22. D.L. Russell, Decay rates for weakly damped systems in Hilbert space obtained with control theoretic methods. J. Differential Equations19 (1975) 344-370.  
23. D.L. Russell, Controllability and stabilizability theory for linear partial differential equations: Recent and open questions. SIAM Rev.20 (1978) 639-739.  
24. H. Triebel, Interpolation theory, function spaces, differential operators. North Holland, Amsterdam (1978).  
25. M. Tucsnak, Regularity and exact controllability for a beam with piezoelectric actuator. SIAM J. Control Optim.34 (1996) 922-930.  
26. M. Tucsnak and G. Weiss, How to get a conservative well posed linear system out of thin air. Preprint.  
27. G.N. Watson, A treatise on the theory of Bessel functions. Cambridge University Press.  
28. G. Weiss, Regular linear systems with feedback. Math. Control Signals Systems7 (1994) 23-57.  

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