Free Access
Volume 4, 1999
Page(s) 419 - 444
Published online 15 August 2002
  1. M. Aassila, On a quasilinear wave equation with a strong damping. Funkcial. Ekvac. 41 (1998) 67-78. [MathSciNet] [Google Scholar]
  2. V. Barbu, Analysis and control of nonlinear infinite dimensional systems. Academic Press, New York (1993). [Google Scholar]
  3. 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]
  4. A. Carpio, Sharp estimates of the energy for the solutions of some dissipative second order evolution equations. Potential Anal. 1 (1992) 265-289. [CrossRef] [MathSciNet] [Google Scholar]
  5. G. Chen, Energy decay estimates and exact boundary value controllability for the wave equation in a bounded domain. J. Math. Pures Appl. 58 (1979) 249-274. [MathSciNet] [Google Scholar]
  6. G. Chen and H. Wang, Asymptotic behavior of solutions of the one dimensional wave equation with a nonlinear boundary stabilizer. SIAM J. Control Optim. 27 (1989) 758-775. [CrossRef] [MathSciNet] [Google Scholar]
  7. F. Chentouh, Décroissance de l'énergie pour certaines équations hyperboliques semilinéaires dissipatives. Thèse de 3Formula cycle, Université Pierre et Marie Curie(1984). [Google Scholar]
  8. F. Conrad, J. Leblond and J. P. Marmorat, Stabilization of second order evolution equations by unbounded nonlinear feedback in. Proc. of the Fifth IFAC Symposium on Control of Distributed Parameter Systems, Perpignan (1989) 101-116. [Google Scholar]
  9. F. Conrad and B. Rao, Decay of solutions of wave equations in a star-shaped domain with non-linear boundary feedback. Asymptotic Analysis 7 (1993) 159-177. [MathSciNet] [Google Scholar]
  10. C.M. Dafermos, Asymptotic behavior of solutions of evolutions equations, Nonlinear evolution equations, M.G. Crandall, Ed., Academic Press, New-York (1978) 103-123. [Google Scholar]
  11. A. Haraux, Comportement à l'infini pour une équation des ondes non linéaire dissipative. C. R. Acad. Sci. Paris Sér. A 287 (1978) 507-509. [Google Scholar]
  12. A. Haraux, Oscillations forcées pour certains systèmes dissipatifs non linéaires. Publication du Laboratoire d'Analyse Numérique No. 78010, Université Pierre et Marie Curie, Paris (1978). [Google Scholar]
  13. A. Haraux and E. Zuazua, Decay estimates for some semilinear damped hyperbolic problems. Arch. Rat. Mech. Anal. 100 (1988) 191-206. [CrossRef] [MathSciNet] [Google Scholar]
  14. M.A. Horn and I. Lasiecka, Global stabilization of a dynamic Von Karman plate with nonlinear boundary feedback. Appl. Math. Optim. 31 (1995) 57-84. [CrossRef] [MathSciNet] [Google Scholar]
  15. M.A. Horn and I. Lasiecka, Nonlinear boundary stabilization of parallelly connected Kirchhoff plates. Dynamics and Control 6 (1996) 263-292. [CrossRef] [MathSciNet] [Google Scholar]
  16. V. Komornik and E. Zuazua, A direct method for the boundary stabilization of the wave equation. J. Maths Pures Appl. 69 (1990) 33-54. [Google Scholar]
  17. V. Komornik, On the nonlinear boundary stabilization of the wave equation. Chinese Ann. Math. Ser. B. 14 (1993) 153-164. [MathSciNet] [Google Scholar]
  18. V. Komornik, Exact Controllability and Stabilization. RAM: Research in Applied Mathematics. Masson, Paris; John Wiley, Ltd., Chichester (1994). [Google Scholar]
  19. S. Kouémou Patcheu, On the decay of solutions of some semilinear hyperbolic problems. Panamer. Math. J. 6 (1996) 69-82. [Google Scholar]
  20. J.E. Lagnese, Decay of solutions of wave equations in a bounded region with boundary dissipation. J. Differential Equations 50 (1983) 163-182. [CrossRef] [MathSciNet] [Google Scholar]
  21. J.E. Lagnese, Boundary stabilization of thin plates. SIAM Studies in Appl. Math., Philadelphia, 1989. [Google Scholar]
  22. I. Lasiecka and D. Tataru, Uniform boundary stabilization of semilinear wave equations with nonlinear boundary damping. J. Diff. Integr. Eq. 6 (1993) 507-533. [Google Scholar]
  23. I. Lasiecka, Uniform stabilizability of a full Von Karman system with nonlinear boundary feedback. SIAM J. Control Optim. 36 (1998) 1376-1422. [CrossRef] [MathSciNet] [Google Scholar]
  24. I. Lasiecka, Boundary stabilization of a 3-dimensional structural acoustic model. J. Math. Pures Appl. 78 (1999) 203-232. [CrossRef] [MathSciNet] [Google Scholar]
  25. J.L. Lions, Contrôlabilité exacte et stabilisation de systèmes distribués, Vol. 1, Masson, Paris (1988). [Google Scholar]
  26. W.-J. Liu and E. Zuazua, Decay rates for dissipative wave equation, preprint. [Google Scholar]
  27. P. Martinez, Decay of solutions of the wave equation with a local highly degenerate dissipation. Asymptotic Analysis 19 (1999) 1-17. [MathSciNet] [Google Scholar]
  28. P. Martinez, A new method to obtain decay rate estimates for dissipative systems with localized damping. Rev. Mat. Compl Madrid, to appear. [Google Scholar]
  29. M. Nakao, Asymptotic stability of the bounded or almost periodic solution of the wave equation with a nonlinear dissipative term. J. Math. Anal. Appl. 58 (1977) 336-343. [CrossRef] [MathSciNet] [Google Scholar]
  30. M. Nakao, Decay of solutions of the wave equation with a local nonlinear dissipation. Math. Ann. 305 (1996) 403-417. [CrossRef] [MathSciNet] [Google Scholar]
  31. L.R. Tcheugoué Tébou, Stabilization of the wave equation with localized nonlinear damping. J. Differential Equations 145 (1998) 502-524. [CrossRef] [MathSciNet] [Google Scholar]
  32. J. Vancostenoble, Optimalité d'estimations d'énergie pour une équation des ondes amortie. C. R. Acad. Sci. Paris Sér. A, to appear. [Google Scholar]
  33. J. Vancostenoble and P. Martinez, Optimality of energy estimates for a damped wave equation with polynomial or non polynomial feedbacks, submitted. [Google Scholar]
  34. E. Zuazua, Stability and decay for a class of nonlinear hyperbolic problems. Asymptotic Analysis 1 (1988) 1-28. [Google Scholar]
  35. E. Zuazua, Uniform stabilization of the wave equation by nonlinear boundary feedback. SIAM J. Control and Optim. 28 (1990) 466-478. [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.