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arXiv · 1410.1122

Finite-time stabilization of a network of strings

Fatiha Alabau-Boussouira·Vincent Perrollaz·Lionel Rosier
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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 $αu_t$ 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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Fatiha Alabau-Boussouira, Vincent Perrollaz, Lionel Rosier. 2014-10-05. Finite-time stabilization of a network of strings. https://arxiv.org/abs/1410.1122

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