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Controllability properties of a vibrating string with variable axial load. (English) Zbl 1175.93032
Summary: 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.

##### MSC:
 93B05 Controllability 35L20 Initial-boundary value problems for second-order hyperbolic equations 74K05 Strings 74M05 Control, switches and devices (“smart materials”) in solid mechanics
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