Free Access
Issue
ESAIM: COCV
Volume 18, Number 2, April-June 2012
Page(s) 548 - 582
DOI https://doi.org/10.1051/cocv/2011106
Published online 14 September 2011
  1. F. Alabau, P. Cannarsa and V. Komornik, Indirect internal damping of coupled systems. J. Evol. Equ. 2 (2002) 127–150. [CrossRef] [MathSciNet] [Google Scholar]
  2. F. Alabau-Boussouira, Stabilisation frontière indirecte de systèmes faiblement couplés. C. R. Acad. Sci. Paris Sér. I Math. 328 (1999) 1015–1020. [CrossRef] [MathSciNet] [Google Scholar]
  3. F. Alabau-Boussouira, Indirect boundary stabilization of weakly coupled systems. SIAM J. Control Optim. 41 (2002) 511–541. [CrossRef] [MathSciNet] [Google Scholar]
  4. F. Alabau-Boussouira, A two-level energy method for indirect boundary observability and controllability of weakly coupled hyperbolic systems. SIAM J. Control Optim. 42 (2003) 871–906. [CrossRef] [MathSciNet] [Google Scholar]
  5. F. Alabau-Boussouira, Une formule générale pour le taux de décroissance des systèmes dissipatifs non linéaires. C. R. Acad. Sci. Paris Sér. I Math. 338 (2004) 35–40. [CrossRef] [Google Scholar]
  6. F. Alabau-Boussouira, Convexity and weighted integral inequalities for energy decay rates of nonlinear dissipative hyperbolic systems. Appl. Math. Optim. 51 (2005) 61–105. [CrossRef] [MathSciNet] [Google Scholar]
  7. F. Alabau-Boussouira, Piecewise multiplier method and nonlinear integral inequalities for Petrowsky equation with nonlinear dissipation. J. Evol. Equ. 6 (2006) 95–112. [CrossRef] [MathSciNet] [Google Scholar]
  8. F. Alabau-Boussouira, Asymptotic behavior for Timoshenko beams subject to a single nonlinear feedback control. NoDEA 14 (2007) 643–669. [CrossRef] [Google Scholar]
  9. F. Ammar-Khodja, A. Benabdallah, J.E. Muñoz Rivera and R. Racke, Energy decay for Timoshenko systems of memory type. J. Differ. Equ. 194 (2003) 82–115. [CrossRef] [Google Scholar]
  10. F. Ammar-Khodja, A. Benabdallah and C. Dupaix, Null controllability of some reaction-diffusion systems with one control force. J. Math. Anal. Appl. 320 (2006) 928–943. [CrossRef] [MathSciNet] [Google Scholar]
  11. 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]
  12. A. Beyrath, Indirect linear locally distributed damping of coupled systems. Bol. Soc. Parana. Math. 22 (2004) 17–34. [Google Scholar]
  13. N. Burq, Décroissance de l’énergie locale de l’équation des ondes pour le problème extérieur et absence de résonance au voisinage du réel. Acta Math. 180 (1998) 1–29. [CrossRef] [MathSciNet] [Google Scholar]
  14. N. Burq and G. Lebeau, Mesures de défaut de compacité, application au système de Lamé. Ann. Sci. Éc. Norm. Supér. 34 (2001) 817–870. [CrossRef] [Google Scholar]
  15. F. Conrad and B. Rao, Decay of solutions of the wave equation in a star-shaped domain with nonlinear boundary feedback. Asymptotic Anal. 7 (1993) 159–177. [Google Scholar]
  16. L. de Teresa, Insensitizing controls for a semilinear heat equation. Commun. Part. Differ. Equ. 25 (2000) 39–72. [CrossRef] [MathSciNet] [Google Scholar]
  17. M. González-Burgos and R. Pérez-García, Controllability results for some nonlinear coupled parabolic systems by one control force. Asymptotic Anal. 46 (2006) 123–162. [Google Scholar]
  18. A. Haraux, Semi-groupes linéaires et équations d’évolution linéaires périodiques. Publication du Laboratoire d’Analyse Numérique, Université Pierre et Marie Curie 78011 (1978) 123–162. [Google Scholar]
  19. O. Kavian and L. de Teresa, Unique continuation principle for systems of parabolic equations. ESAIM : COCV 16 (2010) 247–274. [CrossRef] [EDP Sciences] [Google Scholar]
  20. V. Komornik, Exact controllability and stabilization : The multiplier method. Research in Applied Mathematics 36, Masson, Paris (1994). [Google Scholar]
  21. J.E. Lagnese, Boundary stabilization of thin plates, SIAM Studies in Applied Mathematics 10. SIAM (1989). [Google Scholar]
  22. M. Léautaud, Spectral inequalities for non-selfadjoint elliptic operators and application to the null-controllability of parabolic systems. J. Funct. Anal. 258 (2010) 2739–2778. [CrossRef] [MathSciNet] [Google Scholar]
  23. G. Lebeau, Équation des ondes amorties, in Algebraic and geometric methods in mathematical physics. Math. Phys. Stud., Kluwer Acad. Publ., Dordrecht (1996) 73–109. [Google Scholar]
  24. G. Lebeau and L. Robbiano, Stabilisation de l’équation des ondes par le bord. Duke Math. J. 86 (1997) 465–491. [CrossRef] [MathSciNet] [Google Scholar]
  25. G. Lebeau and E. Zuazua, Decay rates for the three-dimensional linear system of thermoelasticity. Arch. Rational Mech. Anal. 148 (1999) 179–231. [CrossRef] [MathSciNet] [Google Scholar]
  26. J.-L. Lions, Contrôlabilité exacte, perturbations et stabilisation de systèmes distribués, Recherches en Mathématiques Appliquées, Tome 1, 8. Masson, Paris (1988). [Google Scholar]
  27. K. Liu, Locally distributed control and damping for the conservative systems. SIAM J. Control Optim. 35 (1997) 1574–1590. [CrossRef] [MathSciNet] [Google Scholar]
  28. P. Martinez, A new method to obtain decay rate estimates for dissipative systems with localized damping. Rev. Math. Comput. 12 (1999) 251–283. [Google Scholar]
  29. L. Miller, Escape function conditions for the observation, control, and stabilization of the wave equation. SIAM J. Control Optim. 41 (2002) 1554–1566. [CrossRef] [MathSciNet] [Google Scholar]
  30. W. Youssef, Contrôle et stabilisation de systèmes élastiques couplés. Ph. D. thesis, University of Metz, France (2009). [Google Scholar]
  31. E. Zuazua, Exponential decay for the semilinear wave equation with locally distributed damping. Commun. Part. Differ. Equ. 15 (1990) 205–235. [CrossRef] [MathSciNet] [Google Scholar]

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