On the basis properties of the functions arising in the boundary control problem of a string with a variable tension

Sergei A. Avdonin; Boris P. Belinskiy

doi:10.3934/proc.2005.2005.40

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2005, Volume 2005: 40-49. Doi: 10.3934/proc.2005.2005.40 open access

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On the basis properties of the functions arising in the boundary control problem of a string with a variable 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, 2004

Revised: February 28, 2005

Published: August 2005

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Abstract

We consider the boundary control problem for a string. We say that the string is controllable if, by suitable manipulation of the exterior force, the string goes to rest. To prove our controllability results we apply the method of characteristics. Then, using the method of moments we establish a connection between the boundary control problem and the basis property of a system of functions that substitutes the system of nonharmonic exponential functions. The latter system regularly appears in the problems of controllability since the classical papers of H.O. Fattorini and D.L. Russell.

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

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