Geodesic
Remark on stabilization of tree-shaped networks of strings
Applications of Mathematics, Tome 52 (2007) no. 4, pp. 327-343.

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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.
DOI : 10.1007/s10492-007-0018-1
Classification : 35B37, 93B07, 93D15
Keywords: networks of strings; input-output map; well-posed system 
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Ammari, Kaïs; Jellouli, Mohamed. Remark on stabilization of tree-shaped networks of strings. Applications of Mathematics, Tome 52 (2007) no. 4, pp. 327-343. doi : 10.1007/s10492-007-0018-1. http://geodesic.mathdoc.fr/articles/10.1007/s10492-007-0018-1/

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