Abstract
We study small vibrations of a string with a length ℓ(t) varying in time at a speed less than the speed of propagation of vibrations. We establish lower and upper estimates for the energy of the string when a dash-pot with constant damping factor η is placed at the moving boundary. The estimates depend explicitly on ℓ(t),η and a function φ that solves the functional equation φ(t+ℓ(t))−φ(t−ℓ(t))=2.
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