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Article Contents

# Controllability properties of a vibrating string with variable axial load

• 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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