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Controllability of a string under tension

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  • We study controllability for a string under an axial stretching tension. The tension is a sum of a constant positive term and a small, slowly variable, load. We are looking for an exterior force $g(x)f(t)$ that drives the state solution to rest. The controllability problem is reduced to a moment problem for the control $f(t)$: We describe the set of initial data which may be driven to rest by a control $f(t) \in L^2(0, T)$: The description is obtained in terms of the Fourier coefficients of the initial data. The proof is based on an auxiliary basis property result.
    Mathematics Subject Classification: Primary: 93B05, 35C20, 35L20; Secondary: 93C20.


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