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All issues Volume 7 (2002) ESAIM: COCV, 7 (2002) 335-377 References
Free Access
Issue
ESAIM: COCV
Volume 7, 2002
Page(s) 335 - 377
DOI https://doi.org/10.1051/cocv:2002015
Published online 15 September 2002
  1. Z. Artstein and E.F. Infante, On the asymptotic stability of oscillators with unbounded damping. Quart. Appl. Math. 34 (1976) 195-199. [MathSciNet] [Google Scholar]
  2. 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. [Google Scholar]
  3. C. Bardos, G. Lebeau and J. Rauch, Un exemple d'utilisation des notions de propagation pour le contrôle et la stabilisation de problèmes hyperboliques, Nonlinear hyperbolic equations in applied sciences. Rend. Sem. Mat. Univ. Politec. Torino 1988, Special Issue (1989) 11-31. [Google Scholar]
  4. A. Bayliss and E. Turkel, Radiation boundary conditions for wave-like equations. Comm. Pure Appl. Math. 33 (1980) 707-725. [Google Scholar]
  5. A. Benaddi and B. Rao, Energy decay rate of wave equations with indefinite damping. J. Differential Equations 161 (2000) 337-357. [CrossRef] [MathSciNet] [Google Scholar]
  6. C. Castro and S.J. Cox, Achieving arbitrarily large decay in the damped wave equation. SIAM J. Control Optim. 39 (2001) 1748-1755. [CrossRef] [MathSciNet] [Google Scholar]
  7. P. Freitas and E. Zuazua, Stability results for the wave equation with indefinite damping. J. Differential Equations 132 (1996) 338-352. [CrossRef] [MathSciNet] [Google Scholar]
  8. A. Haraux, Une remarque sur la stabilisation de certains systèmes du deuxième ordre en temps, Publications du Laboratoire d'Analyse numérique. Université Pierre et Marie Curie (1988). [Google Scholar]
  9. A. Haraux, A generalized internal control for the wave equation in a rectangle. J. Math. Anal. Appl. 153 (1990) 190-216. [CrossRef] [MathSciNet] [Google Scholar]
  10. W.A. Harris Jr., P. Pucci and J. Serrin, Asymptotic behavior of solutions of a nonstandard second order differential equation. Differential Integral Equations 6 (1993) 1201-1215. [MathSciNet] [Google Scholar]
  11. L. Hatvani, On the stability of the zero solution of second order nonlinear differential equations. Acta Sci. Math. 32 (1971) 1-9. [Google Scholar]
  12. L. Hatvani and V. Totik, Asymptotic stability of the equilibrium of the damped oscillator. Differential Integral Equation 6 (1993) 835-848. [Google Scholar]
  13. L. Hatvani, T. Krisztin, V. Totik and Vilmos, A necessary and sufficient condition for the asymptotic stability of the damped oscillator. J. Differential Equations 119 (1995) 209-223. [CrossRef] [MathSciNet] [Google Scholar]
  14. 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]
  15. V. Komornik and E. Zuazua A direct method for boundary stabilization of the wave equation. J. Math. Pures Appl. 69 (1990) 33-54. [Google Scholar]
  16. V. Komornik, Exact Controllability and Stabilization. The Multiplier Method. John Wiley, Chicester and Masson, Paris (1994). [Google Scholar]
  17. J. Lagnese, Decay of solutions of wave equations in a bounded region with boundary dissipation. J. Differential Equations 50 (1983) 163-182. [Google Scholar]
  18. J. Lagnese, Note on boundary stabilization of wave equation. SIAM J. Control Optim. 26 (1988) 1250-1256. [CrossRef] [MathSciNet] [Google Scholar]
  19. I. Lasiecka and R. Triggiani, Uniform exponential decay in a bounded region with Formula -feedback control in the Dirichlet boundary condition. J. Differential Equations 66 (1987) 340-390. [Google Scholar]
  20. I. Lasiecka and R. Triggiani, Uniform stabilization of the wave equation with Dirichlet or Neumann feedback control without geometrical conditions. Appl. Math. Optim. 25 (1992) 189-224. [CrossRef] [MathSciNet] [Google Scholar]
  21. J.-L. Lions, Contrôlabilité exacte de systèmes distribués. C. R. Acad. Sci. Paris 302 (1986) 471-475. [Google Scholar]
  22. J.-L. Lions, Contrôlabilité exacte, stabilisation et perturbations de systèmes distribués. Masson, RMA 8 (1988). [Google Scholar]
  23. J.-L. Lions, Exact controllability, stabilization adn perturbations for distributd systems. SIAM Rev. 30 (1988) 1-68. [CrossRef] [MathSciNet] [Google Scholar]
  24. S. Marakuni, Asymptotic behavior of solutions of one-dimensional damped wave equations. Comm. Appl. Nonlin. Anal. 1 (1999) 99-116. [Google Scholar]
  25. P. Martinez, Precise decay rate estimates for time-dependent dissipative systems. Israël J. Math. 119 (2000) 291-324. [CrossRef] [MathSciNet] [Google Scholar]
  26. P. Martinez and J. Vancostenoble, Exact controllability in ``arbitrarily short time" of the semilinear wave equation. Discrete Contin. Dynam. Systems (to appear). [Google Scholar]
  27. M. Nakao, On the time decay of solutions of the wave equation with a local time-dependent nonlinear dissipation. Adv. Math. Sci. Appl. 7 (1997) 317-331. [MathSciNet] [Google Scholar]
  28. K. Petersen, Ergodic Theory. Cambridge University Press, Cambridge, Studies in Adv. Math. 2 (1983). [Google Scholar]
  29. P. Pucci and J. Serrin, Precise damping conditions for global asymptotic stability for nonlinear second order systems. Acta Math. 170 (1993) 275-307. [CrossRef] [MathSciNet] [Google Scholar]
  30. P. Pucci and J. Serrin, Precise damping conditions for global asymptotic stability for nonlinear second order systems, II. J. Differential Equations 113 (1994) 505-534. [CrossRef] [MathSciNet] [Google Scholar]
  31. P. Pucci and J. Serrin, Asymptotic stability for intermittently controlled nonlinear oscillators. SIAM J. Math. Anal. 25 (1994) 815-835. [CrossRef] [MathSciNet] [Google Scholar]
  32. P. Pucci and J. Serrin, Asymptotic stability for nonautonomous dissipative wave systems. Comm. Pure Appl. Math. XLIX (1996) 177-216. [Google Scholar]
  33. P. Pucci and J. Serrin, Local asymptotic stability for dissipative wave systems. Israël J. Math. 104 (1998) 29-50. [CrossRef] [MathSciNet] [Google Scholar]
  34. R.A. Smith, Asymptotic stability of x''+a(t)x'+x=0. Quart. J. Math. Oxford (2) 12 (1961) 123-126. [CrossRef] [Google Scholar]
  35. L.H. Thurston and J.W. Wong, On global asymptotic stability of certain second order differential equations with integrable forcing terms. SIAM J. Appl. Math. 24 (1973) 50-61. [CrossRef] [MathSciNet] [Google Scholar]
  36. J. Vancostenoble and P. Martinez, Optimality of energy estimates for the wave equation with nonlinear boundary velocity feedbacks. SIAM J. Control Optim. 39 (2000) 776-797. [CrossRef] [MathSciNet] [Google Scholar]
  37. E. Zuazua, An introduction to the exact controllability for distributed systems, Textos et Notas 44, CMAF. Universidades de Lisboa (1990). [Google Scholar]

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