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. Our results lead to the finite-time stabilization even though the systems may not be dissipative.
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https://hal-mines-paristech.archives-ouvertes.fr/hal-01261807
Contributeur : François Chaplais <>
Soumis le : lundi 25 janvier 2016 - 17:23:59
Dernière modification le : lundi 12 novembre 2018 - 11:03:50

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Fatiha Alabau-Boussouira, Vincent Perrollaz, Lionel Rosier. Finite-time stabilization of a network of strings. Mathematical Control and Related Fields, AIMS, 2015, 5 (4), pp.721 - 742. ⟨10.3934/mcrf.2015.5.721⟩. ⟨hal-01261807⟩

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