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

Bopeng Rao; Zhuangyi Liu

doi:10.3934/dcds.2009.23.399

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2009, Volume 23, Issue 1&2: 399-414. Doi: 10.3934/dcds.2009.23.399

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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
2.
Institut de Recherche Mathématique Avancée, Université Louis Pasteur de Strasbourg, 7 rue René-Descartes, 67084 Strasbourg

Received: November 30, 2007

Revised: July 31, 2008

Published: April 2009

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Abstract

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.

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Mathematics Subject Classification: Primary: 93B07; Secondary: 93B05.

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