Exponential stability estimates for an axially travelling string damped at one end
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Date
2023
Journal Title
Journal ISSN
Volume Title
Publisher
université msila
Abstract
We study the small vibrations of an axially travelling string with a dashpot
damping at one end. The string is modelled by a wave equation in a timedependent interval with two endpoints moving at a constant speed v. For
the undamped case, we obtain a conserved functional equivalent to the
energy of the solution. We derive precise upper and lower exponentially
decaying estimates for the energy with explicit constants. These estimates
do not seem to be reported in the literature even for the non-travelling case
v = 0
Description
Keywords
Axially travelling strings; Fourier series; energy estimates; boundary stabilisation