Seyf Eddine GhenimiAbdelmouhcene Sengouga2023-07-112023-07-112023http://dspace.univ-msila.dz:8080//xmlui/handle/123456789/40333We 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 = 0Axially travelling strings; Fourier series; energy estimates; boundary stabilisationArticle