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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 827698, 6 pages
http://dx.doi.org/10.1155/2014/827698
Research Article

Controllability for a Wave Equation with Moving Boundary

1College of Applied Mathematics, Jilin University of Finance and Economics, Changchun 130117, China
2School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China
3Educational Administration, Jilin University of Finance and Economics, Changchun 130117, China

Received 8 November 2013; Accepted 15 February 2014; Published 27 February 2014

Academic Editor: Laurent Gosse

Copyright © 2014 Lizhi Cui and Libo Song. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We investigate the controllability for a one-dimensional wave equation in domains with moving boundary. This model characterizes small vibrations of a stretched elastic string when one of the two endpoints varies. When the speed of the moving endpoint is less than , by Hilbert uniqueness method, sidewise energy estimates method, and multiplier method, we get partial Dirichlet boundary controllability. Moreover, we will give a sharper estimate on controllability time that only depends on the speed of the moving endpoint.