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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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