Stabilization of Generic Trees of Strings

Authors:
Kais Ammari;Mohamed Jellouli;Moez Khenissi
Affiliations:
Department of Mathematics, Faculty of Sciences of Monastir, Monastir, Tunisia 5019;Department of Mathematics, Faculty of Sciences of Monastir, Monastir, Tunisia 5019;Department of Mathematics, Faculty of Sciences of Monastir, Monastir, Tunisia 5019
Venue:
Journal of Dynamical and Control Systems
Year:
2005

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Abstract

We study the energy decay of a tree-shaped network of vibrating elastic strings when the pointwise feedback acts in the root of the tree. We show that the strings are not exponentially stable in the energy space. Moreover, we give explicit polynomial decay estimates valid for regular initial data.