Free Access
Volume 18, Number 1, January-March 2012
Page(s) 208 - 228
Published online 02 December 2010
  1. K. Ammari and M. Jellouli, Stabilization of star-shaped tree of elastic strings. Differential Integral Equations 17 (2004) 1395–1410. [MathSciNet]
  2. K. Ammari and M. Jellouli, Remark on stabilization of tree-shaped networks of strings. Appl. Math. 52 (2007) 327–343. [CrossRef] [MathSciNet]
  3. K. Ammari and S. Nicaise, Polynomial and analytic stabilization of a wave equation coupled with a Euler-Bernoulli beam. Math. Methods Appl. Sci. 32 (2009) 556–576. [CrossRef] [MathSciNet]
  4. K. Ammari, M. Jellouli and M. Khenissi, Stabilization of generic trees of strings. J. Dyn. Control Syst. 11 (2005) 177–193. [CrossRef] [MathSciNet]
  5. J.A. Bondy and U.S.R. Murty, Graph Theory, Graduate Texts in Mathematics Series. Springer-Verlag, New York (2008).
  6. R. Dáger, Observation and control of vibrations in tree-shaped networks of strings. SIAM J. Control Optim. 43 (2004) 590–623. [CrossRef] [MathSciNet]
  7. R. Dáger and E. Zuazua, Controllability of star-shaped networks of strings. C. R. Acad. Sci. Paris, Sér. I 332 (2001) 621–626.
  8. R. Dáger and E. Zuazua, Controllability of tree-shaped networks of vibrating strings. C. R. Acad. Sci. Paris, Sér. I 332 (2001) 1087–1092.
  9. R. Dáger and E. Zuazua, Wave propagation, observation and control in 1-d flexible multistructures, Mathématiques and Applications 50. Springer-Verlag, Berlin (2006).
  10. M. Gugat, Boundary feedback stabilization by time delay for one-dimensional wave equations. IMA J. Math. Control Inform. 27 (2010) 189–204. [CrossRef] [MathSciNet]
  11. B.Z. Guo and Z.C. Shao, On exponential stability of a semilinear wave equation with variable coefficients under the nonlinear boundary feedback. Nonlinear Anal. 71 (2009) 5961–5978. [CrossRef] [MathSciNet]
  12. D. Jungnickel, Graphs, Networks and Algorithms, Algorithms and Computation in Mathematics 5. Springer-Verlag, New York, third edition (2008).
  13. J.E. Lagnese, G. Leugering and E.J.P.G. Schmidt, Modeling, analysis and control of dynamic elastic multi-link structures – Systems and control : Foundations and applications. Birkhäuser-Basel (1994).
  14. G. Leugering and E.J.P.G. Schmidt, On the control of networks of vibrating strings and beams. Proc. of the 28th IEEE Conference on Decision and Control 3 (1989) 2287–2290. [CrossRef]
  15. G. Leugering and E. Zuazua, On exact controllability of generic trees. ESAIM : Proc. 8 (2000) 95–105. [CrossRef] [EDP Sciences]
  16. Yu.I. Lyubich and V.Q. Phóng, Asymptotic stability of linear differential equations in Banach spaces. Studia Math. 88 (1988) 34–37.
  17. S. Nicaise and J. Valein, Stabilization of the wave equation on 1-d networks with a delay term in the nodal feedbacks. Netw. Heterog. Media 2 (2007) 425-479. [CrossRef] [MathSciNet]
  18. A. Pazy, Semigroups of linear operators and applications to partial differential equations. Springer-Verlag, Berlin (1983).
  19. J. Valein and E. Zuazua, Stabilization of the wave equation on 1-d networks. SIAM J. Control Optim. 48 (2009) 2771–2797. [CrossRef] [MathSciNet]
  20. G.Q. Xu, D.Y. Liu and Y.Q. Liu, Abstract second order hyperbolic system and applications to controlled network of strings. SIAM J. Control Optim. 47 (2008) 1762–1784. [CrossRef] [MathSciNet]

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.