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

Pages: 399 - 414, Volume 23, Issue 1/2, January/February 2009

doi:10.3934/dcds.2009.23.399       Abstract        Full Text (221.2K)       Related Articles

Zhuangyi Liu - Department of Mathematics and Statistics, University of Minnesota, Duluth, MN 55812-2496, United States (email)
Bopeng Rao - Institut de Recherche Mathématique Avancée, Université Louis Pasteur de Strasbourg, 7 rue René-Descartes, 67084 Strasbourg, France (email)

Abstract: 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.

Keywords:  Ingham's inequality, non harmonic analysis, weak observability, exact controllability
Mathematics Subject Classification:  Primary: 93B07; Secondary: 93B05

Received: December 2007;      Revised: August 2008;      Published: September 2008.