Free Access
Issue
ESAIM: COCV
Volume 14, Number 3, July-September 2008
Page(s) 561 - 574
DOI https://doi.org/10.1051/cocv:2007066
Published online 21 December 2007
  1. C. Bardos, G. Lebeau and J. Rauch, Sharp sufficient conditions for the observation, control and stabilization from the boundary. SIAM J. Control Opt. 30 (1992) 1024–1065. [CrossRef] [MathSciNet] [Google Scholar]
  2. M.E. Bradley and I. Lasiecka, Global decay rates for the solutions to a von Kármán plate without geometric conditions. J. Math. Anal. Appl. 181 (1994) 254–276. [CrossRef] [MathSciNet] [Google Scholar]
  3. H. Brezis, Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. North-Holland (1973). [Google Scholar]
  4. H. Brezis, Analyse fonctionnelle. Théorie et Applications. Masson, Paris (1983). [Google Scholar]
  5. G. Chen, S.A. Fulling, F.J. Narcowich and S. Sun, Exponential decay of energy of evolution equations with locally distributed damping. SIAM J. Appl. Math. 51 (1991) 266–301. [CrossRef] [MathSciNet] [Google Scholar]
  6. C.M. Dafermos, Asymptotic behaviour of solutions of evolution equations, in Nonlinear evolution equations, M.G. Crandall Ed., Academic Press, New-York (1978) 103–123. [Google Scholar]
  7. B. Dehman, Stabilisation pour l'équation des ondes semi-linéaire. Asymptotic Anal. 27 (2001) 171–181. [Google Scholar]
  8. B. Dehman, G. Lebeau and E. Zuazua, Stabilization and control for the subcritical semilinear wave equation. Ann. Sci. École Norm. Sup. 36 (2003) 525–551. [Google Scholar]
  9. A. Doubova and A. Osses, Rotated weights in global Carleman estimates applied to an inverse problem for the wave equation. Inverse Problems 22 (2006) 265–296. [CrossRef] [MathSciNet] [Google Scholar]
  10. T. Duyckaerts, X. Zhang and E. Zuazua, On the optimality of the observability for parabolic and hyperbolic systems with potentials. Ann. Inst. H. Poincaré Anal. Non Linéaire (to appear). [Google Scholar]
  11. X. Fu, J. Yong and X. Zhang, Exact controllability for multidimensional semilinear hyperbolic equations. SIAM J. Contr. Opt. 46 (2007) 1578–1614. [CrossRef] [MathSciNet] [Google Scholar]
  12. A. Haraux, Stabilization of trajectories for some weakly damped hyperbolic equations. J. Diff. Eq. 59 (1985) 145–154. [CrossRef] [MathSciNet] [Google Scholar]
  13. A. Haraux, Semi-linear hyperbolic problems in bounded domains, in Mathematical Reports 3, Hardwood academic publishers (1987) . [Google Scholar]
  14. A. Haraux, Une remarque sur la stabilisation de certains systèmes du deuxième ordre en temps. Portugal. Math. 46 (1989) 245–258. [MathSciNet] [Google Scholar]
  15. A. Haraux, Remarks on weak stabilization of semilinear wave equations. ESAIM: COCV 6 (2001) 553–560. [CrossRef] [EDP Sciences] [Google Scholar]
  16. O.Yu. Imanuvilov, On Carleman estimates for hyperbolic equations. Asympt. Anal. 32 (2002) 185–220. [Google Scholar]
  17. V. Komornik, Exact controllability and stabilization. The multiplier method. RAM, Masson & John Wiley, Paris (1994). [Google Scholar]
  18. J. Lagnese, Control of wave processes with distributed control supported on a subregion. SIAM J. Control Opt. 21 (1983) 68–85. [CrossRef] [Google Scholar]
  19. I. Lasiecka and D. Tataru, Uniform boundary stabilization of semilinear wave equations with nonlinear boundary damping. Differential Integral Equations 6 (1993) 507–533. [MathSciNet] [Google Scholar]
  20. J.-L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod-Gauthier-Villars, Paris (1969). [Google Scholar]
  21. J.-L. Lions, Contrôlabilité exacte, perturbations et stabilisation des systèmes distribués, Vol. 1, RMA 8. Masson, Paris (1988). [Google Scholar]
  22. J.-L. Lions and E. Magenes, Non-homogeneous boundary value problems and applications, Vol. I. Springer-Verlag, New York-Heidelberg (1973). [Google Scholar]
  23. K. Liu, Locally distributed control and damping for the conservative systems. SIAM J. Control Opt. 35 (1997) 1574–1590. [CrossRef] [MathSciNet] [Google Scholar]
  24. F. Macià and E. Zuazua, On the lack of observability for wave equations: a gaussian beam approach. Asymptot. Anal. 32 (2002) 1–26. [MathSciNet] [Google Scholar]
  25. P. Martinez, Ph.D. thesis, University of Strasbourg, France (1998). [Google Scholar]
  26. P. Martinez, A new method to obtain decay rate estimates for dissipative systems with localized damping. Rev. Mat. Complut. 12 (1999) 251–283. [MathSciNet] [Google Scholar]
  27. M. Nakao, Decay of solutions of the wave equation with a local degenerate dissipation. Israel J. Math. 95 (1996) 25–42. [CrossRef] [MathSciNet] [Google Scholar]
  28. M. Nakao, Global existence for semilinear wave equations in exterior domains, in Proceedings of the Third World Congress of Nonlinear Analysts, Part 4 (Catania, 2000), Nonlinear Anal. 47 (2001) 2497–2506. [Google Scholar]
  29. M. Nakao, Global and periodic solutions for nonlinear wave equations with some localized nonlinear dissipation. J. Diff. Eq. 190 (2003) 81–107. [CrossRef] [Google Scholar]
  30. M. Nakao and I.H. Jung, Energy decay for the wave equation in exterior domains with some half-linear dissipation. Differential Integral Equations 16 (2003) 927–948. [MathSciNet] [Google Scholar]
  31. A. Pazy, Semigroups of linear operators and applications to partial differential equations, Applied Mathematical Sciences 44. Springer-Verlag, New York (1983). [Google Scholar]
  32. G. Perla Menzala and E. Zuazua, The energy decay rate for the modified von Kármán system of thermoelastic plates: an improvement. Appl. Math. Lett. 16 (2003) 531–534. [CrossRef] [MathSciNet] [Google Scholar]
  33. A. Ruiz, Unique continuation for weak solutions of the wave equation plus a potential. J. Math. Pures Appl. 71 (1992) 455–467. [MathSciNet] [Google Scholar]
  34. D.L. Russell, Exact boundary value controllability theorems for wave and heat processes in star-complemented regions, in Differential games and control theory (Proc. NSF—CBMS Regional Res. Conf., Univ. Rhode Island, Kingston, R.I., 1973) Dekker, New York. Lect. Notes Pure Appl. Math. 10, Dekker, New York (1974) 291–319. [Google Scholar]
  35. M. Slemrod, Weak asymptotic decay via a relaxed invariance principle for a wave equation with nonlinear, nonmonotone damping. Proc. Royal Soc. Edinburgh Sect. A 113 (1989) 87–97. [Google Scholar]
  36. D. Tataru, The Formula spaces and unique continuation for solutions to the semilinear wave equation. Comm. Partial Differential Equations 21 (1996) 841–887. [CrossRef] [MathSciNet] [Google Scholar]
  37. L.R. Tcheugoué Tébou, Estimations d'énergie pour l'équation des ondes avec un amortissement nonlinéaire localisé. C. R. Acad. Paris, Sér. I 325 (1997) 1175–1179. [Google Scholar]
  38. L.R. Tcheugoué Tébou, On the decay estimates for the wave equation with a local degenerate or nondegenerate dissipation. Portugal. Math. 55 (1998) 293–306. [MathSciNet] [Google Scholar]
  39. L.R. Tcheugoué Tébou, Stabilization of the wave equation with localized nonlinear damping. J. Diff. Eq. 145 (1998) 502–524 [CrossRef] [MathSciNet] [Google Scholar]
  40. L.R. Tcheugoué Tébou, Well-posedness and energy decay estimates for the damped wave equation with Lr localizing coefficient. Comm. Partial Differential Equations 23 (1998) 1839–1855. [MathSciNet] [Google Scholar]
  41. L.R. Tcheugoué Tébou, A direct method for the stabilization of some locally damped semilinear wave equations. C. R. Acad. Sci. Paris, Ser. I 342 (2006) 859–864. [Google Scholar]
  42. J. Vancostenoble, Stabilisation non monotone de systèmes vibrants et Contrôlabilité. Ph.D. thesis, University of Rennes, France (1998). [Google Scholar]
  43. J. Vancostenoble, Weak asymptotic decay for a wave equation with gradient dependent damping. Asymptot. Anal. 26 (2001) 1–20. [MathSciNet] [Google Scholar]
  44. X. Zhang and E. Zuazua, On the optimality of the observability inequalities for Kirchhoff plate systems with potentials in unbounded domains, in Proceedings of the Eleventh International Conference on Hyperbolic Problems: Theory, Numerics and Applications, Lyon (2006) (to appear). [Google Scholar]
  45. E. Zuazua, Exponential decay for the semilinear wave equation with locally distributed damping. Comm. Partial Differential Equations 15 (1990) 205–235. [CrossRef] [MathSciNet] [Google Scholar]
  46. E. Zuazua, Exponential decay for the semilinear wave equation with localized damping in unbounded domains. J. Math. Pures Appl. 15 (1990) 205–235. [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.