# American Institute of Mathematical Sciences

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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

 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 two weakly coupled one-dimensional wave equations with the control acted on only one equation. Using the non harmonic analysis, we establish the weak observability inequalities, which depend on the ratio of the wave propagation speeds. The obtained results are optimal.
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 - A, 2009, 23 (1&2) : 399-414. doi: 10.3934/dcds.2009.23.399
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