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Applications of Mathematics

, Volume 52, Issue 4, pp 327–343 | Cite as

Remark on stabilization of tree-shaped networks of strings

  • Kaïs Ammari
  • Mohamed Jellouli
Article

Abstract

We consider a tree-shaped network of vibrating elastic strings, with feedback acting on the root of the tree. Using the d’Alembert representation formula, we show that the input-output map is bounded, i.e. this system is a well-posed system in the sense of G. Weiss (Trans. Am. Math. Soc. 342 (1994), 827–854). As a consequence we prove that the strings networks are not exponentially stable in the energy space. Moreover, we give explicit polynomial decay estimates valid for regular initial data.

Keywords

networks of strings input-output map well-posed system 

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Copyright information

© Mathematical Institute, Academy of Sciences of Czech Republic 2007

Authors and Affiliations

  • Kaïs Ammari
    • 1
  • Mohamed Jellouli
    • 1
  1. 1.Department of MathematicsFaculty of Sciences of MonastirMonastirTunisia

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