Finite-time stabilization of a network of strings - Archive ouverte HAL Access content directly
Journal Articles Mathematical Control and Related Fields Year : 2015

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 $\alpha u_t$ with a coefficient $\alpha$ that may depend on the node is considered. We show that for a convenient choice of the sequence of coefficients $\alpha$, 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.
Fichier principal
Vignette du fichier
APR.pdf (407.82 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01071150 , version 1 (03-10-2014)

Identifiers

Cite

Fatiha Alabau-Boussouira, Vincent Perrollaz, Lionel Rosier. Finite-time stabilization of a network of strings. Mathematical Control and Related Fields, 2015, 5 (4), pp.721-742. ⟨10.3934/mcrf.2015.5.721⟩. ⟨hal-01071150⟩
598 View
172 Download

Altmetric

Share

Gmail Facebook X LinkedIn More