EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 18 / No 2 (April-June 2012) ESAIM: COCV, 18 2 (2012) 548-582 References
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. [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. [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. [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. [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. [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. [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. [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]

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.