Controllability of a string under tension

Sergei A. Avdonin; Boris P. Belinskiy

doi:10.3934/proc.2003.2003.57

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2003, Volume 2003: 57-67. Doi: 10.3934/proc.2003.2003.57 open access

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Controllability of a string under tension

Sergei A. Avdonin^1, and
Boris P. Belinskiy^2,

1.
University of Alaska Fairbanks, Fairbanks, AK 99775-6660
2.
Department of Mathematics, University of Tennessee at Chattanooga, 615 McCallie Avenue, Chattanooga, TN 37403-2598

Received: August 31, 2002

Revised: February 28, 2003

Published: March 2003

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Abstract

We study controllability for a string under an axial stretching tension. The tension is a sum of a constant positive term and a small, slowly variable, load. We are looking for an exterior force $g(x)f(t)$ that drives the state solution to rest. The controllability problem is reduced to a moment problem for the control $f(t)$: We describe the set of initial data which may be driven to rest by a control $f(t) \in L^2(0, T)$: The description is obtained in terms of the Fourier coefficients of the initial data. The proof is based on an auxiliary basis property result.

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Mathematics Subject Classification: Primary: 93B05, 35C20, 35L20; Secondary: 93C20.

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