Stability of a Nonlinear Axially Moving String With the Kelvin-Voigt Damping

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dc.creatorShahruz, Shahram M.
dc.date2007-10-03
dc.date.accessioned2026-07-07T08:33:48Z
dc.date.available2026-07-07T08:33:48Z
dc.descriptionIn this paper, a nonlinear axially moving string with the Kelvin-Voigt damping is considered. It is proved that the string is stable, i.e., its transversal displacement converges to zero when the axial speed of the string is less than a certain critical value. The proof is established by showing that a Lyapunov function corresponding to the string decays to zero exponentially. It is also shown that the string displacement is bounded when a bounded distributed force is applied to it transversally. Furthermore, a few open problems regarding the stability and stabilization of strings with the Kelvin-Voigt damping are stated.
dc.description15 pages. 1 figure
dc.identifierhttps://arxiv.org/abs/0710.0872
dc.identifierhttp://arxiv.org/abs/0710.0872
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/139258
dc.subjectAnalysis of PDEs
dc.titleStability of a Nonlinear Axially Moving String With the Kelvin-Voigt Damping
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