Finite-time stabilization of a network of strings

Abstract

We investigate the finite-time stabilization of a tree-shaped network of strings. Transparent boundary conditions are applied at all the external nodes. At any internal node, in addition to the usual continuity conditions, a modified Kirchhoff law incorporating a damping term αut with a coefficient α that may depend on the node is considered. We show that for a convenient choice of the sequence of coefficients α, any solution of the wave equation on the network becomes constant after a finite time. The condition on the coefficients proves to be sharp at least for a star-shaped tree. Similar results are derived when we replace the transparent boundary condition by the Dirichlet (resp. Neumann) boundary condition at one external node.

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Cite this paper

@inproceedings{AlabauBoussouira2017FinitetimeSO, title={Finite-time stabilization of a network of strings}, author={Fatiha Alabau-Boussouira and Vincent Perrollaz and Lionel Rosier}, year={2017} }