Free Access
Issue
ESAIM: COCV
Volume 6, 2001
Page(s) 361 - 386
DOI https://doi.org/10.1051/cocv:2001114
Published online 15 August 2002
  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. [CrossRef] [MathSciNet] [Google Scholar]
  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. [Google Scholar]
  3. A. Bamberger, J. Rauch and M. Taylor, A model for harmonics on stringed instruments. Arch. Rational Mech. Anal. 79 (1982) 267-290. [MathSciNet] [Google Scholar]
  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. [Google Scholar]
  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. [CrossRef] [MathSciNet] [Google Scholar]
  6. A. Bensoussan, G. Da Prato, M.C. Delfour and S.K. Mitter, Representation and control of infinite Dimensional Systems, Vol. I. Birkhauser (1992). [Google Scholar]
  7. J.W.S. Cassals, An introduction to Diophantine Approximation. Cambridge University Press, Cambridge (1966). [Google Scholar]
  8. G. Doetsch, Introduction to the theory and application of the Laplace transformation. Springer, Berlin (1974). [Google Scholar]
  9. A. Haraux, Une remarque sur la stabilisation de certains systèmes du deuxième ordre en temps. Portugal Math. 46 (1989) 245-258. [MathSciNet] [Google Scholar]
  10. A.E. Ingham, Some trigonometrical inequalities with applications in the theory of series. Math. Z. 41 (1936) 367-369. [CrossRef] [MathSciNet] [Google Scholar]
  11. S. Jaffard, M. Tucsnak and E. Zuazua, Singular internal stabilization of the wave equation. J. Differential Equations 145 (1998) 184-215. [CrossRef] [MathSciNet] [Google Scholar]
  12. V. Komornik, Rapid boundary stabilization of linear distributed systems. SIAM J. Control Optim. 35 (1997) 1591-1613. [CrossRef] [MathSciNet] [Google Scholar]
  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. [MathSciNet] [Google Scholar]
  14. J. Lagnese, Boundary stabilization of thin plates. Philadelphia, SIAM Stud. Appl. Math. (1989). [Google Scholar]
  15. S. Lang, Introduction to diophantine approximations. Addison Wesley, New York (1966). [Google Scholar]
  16. J.L. Lions, Contrôlabilité exacte des systèmes distribués. Masson, Paris (1998). [Google Scholar]
  17. J.L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications, Vol. 1. Dunod, Paris (1968). [Google Scholar]
  18. F.W.J. Olver, Asymptotic and Special Functions. Academic Press, New York. [Google Scholar]
  19. A. Pazy, Semigroups of linear operators and applications to partial differential equations. Springer, New York (1983). [Google Scholar]
  20. R. Rebarber, Exponential stability of beams with dissipative joints: A frequency approach. SIAM J. Control Optim. 33 (1995) 1-28. [CrossRef] [MathSciNet] [Google Scholar]
  21. L. Robbiano, Fonction de coût et contrôle des solutions des équations hyperboliques. Asymptot. Anal. 10 (1995) 95-115. [Google Scholar]
  22. D.L. Russell, Decay rates for weakly damped systems in Hilbert space obtained with control theoretic methods. J. Differential Equations 19 (1975) 344-370. [CrossRef] [MathSciNet] [Google Scholar]
  23. D.L. Russell, Controllability and stabilizability theory for linear partial differential equations: Recent and open questions. SIAM Rev. 20 (1978) 639-739. [CrossRef] [MathSciNet] [Google Scholar]
  24. H. Triebel, Interpolation theory, function spaces, differential operators. North Holland, Amsterdam (1978). [Google Scholar]
  25. M. Tucsnak, Regularity and exact controllability for a beam with piezoelectric actuator. SIAM J. Control Optim. 34 (1996) 922-930. [CrossRef] [MathSciNet] [Google Scholar]
  26. M. Tucsnak and G. Weiss, How to get a conservative well posed linear system out of thin air. Preprint. [Google Scholar]
  27. G.N. Watson, A treatise on the theory of Bessel functions. Cambridge University Press. [Google Scholar]
  28. G. Weiss, Regular linear systems with feedback. Math. Control Signals Systems 7 (1994) 23-57. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.