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2005, 2005(Special): 40-49. doi: 10.3934/proc.2005.2005.40

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, United States
2. 

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

Received  September 2004 Revised  March 2005 Published  September 2005

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.
Keywords: Riesz basis, hyperbolic equation, Distributed parameter systems, characteristics., boundary control.
Mathematics Subject Classification: Primary: 93B05; Secondary: 35C20, 35L2.
Citation: Sergei A. Avdonin, Boris P. Belinskiy. On the basis properties of the functions arising in the boundary control problem of a string with a variable tension. Conference Publications, 2005, 2005 (Special) : 40-49. doi: 10.3934/proc.2005.2005.40
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