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

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

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