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Controllability properties of a vibrating string with variable axial load

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  • We show that the set of equilibrium-like states $ (y_d, 0) $ of a vibrating string which can approximately be reached in the energy space $ H_0^1 (0,1) \times L^2 (0,1) $ from almost any non-zero initial datum by varying its axial load is dense in the subspace $ H_0^1 (0,1) \times $ {0} of this space. Our result is based on a constructive argument and makes use of piecewise constant-in-time control functions (loads) only, which enter the model equation as coefficients.
    Mathematics Subject Classification: 93, 35.

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