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February  2009, 23(1&2): 399-414. doi: 10.3934/dcds.2009.23.399

A spectral approach to the indirect boundary control of a system of weakly coupled wave equations

Bopeng Rao 2, and  Zhuangyi Liu 1,

1. 

Department of Mathematics and Statistics, University of Minnesota, Duluth, MN 55812-2496, United States
2. 

Institut de Recherche Mathématique Avancée, Université Louis Pasteur de Strasbourg, 7 rue René-Descartes, 67084 Strasbourg

Received  December 2007 Revised  August 2008 Published  September 2008

In this paper, we study the exact controllability of a system of twoweakly coupled one-dimensional wave equations with the control actedon only one equation. Using the non harmonic analysis, we establishthe weak observability inequalities, which depend on the ratio ofthe wave propagation speeds. The obtained results are optimal.
Keywords: exact controllability, weak observability, Ingham's inequality, non harmonic analysis.
Mathematics Subject Classification: Primary: 93B07; Secondary: 93B05.
Citation: Bopeng Rao, Zhuangyi Liu. A spectral approach to the indirect boundary control of a system of weakly coupled wave equations. Discrete & Continuous Dynamical Systems, 2009, 23 (1&2) : 399-414. doi: 10.3934/dcds.2009.23.399
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