American Institute of Mathematical Sciences

Advanced
2003, 2003(Special): 57-67. doi: 10.3934/proc.2003.2003.57

Controllability of a string under tension

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

1. 

University of Alaska Fairbanks, Fairbanks, AK 99775-6660, United States
2. 

Department of Mathematics, University of Tennessee at Chattanooga, 615 McCallie Avenue, Chattanooga, TN 37403-2598, United States

Received  September 2002 Revised  March 2003 Published  April 2003

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.
Keywords: moment problem., Riesz basis, string equation, exact controllability.
Mathematics Subject Classification: Primary: 93B05, 35C20, 35L20; Secondary: 93C2.
Citation: Sergei A. Avdonin, Boris P. Belinskiy. Controllability of a string under tension. Conference Publications, 2003, 2003 (Special) : 57-67. doi: 10.3934/proc.2003.2003.57
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