Abstract
In this paper initial-boundary value problems for a linear, and a weakly nonlinear string (or wave) equation are considered. One end of the string is assumed to be fixed and the other end of the string is attached to a spring-mass-dashpot system, where the damping generated by the dashpot is assumed to be small. This problem can be regarded as a simple model describing oscillations of flexible structures such as overhead power transmission lines. For a linear problem a semigroup approach will be used to show the well-posedness of the problem as well as the asymptotic validity of formal approximations of the solution on long time-scales. It is also shown hov a multiple time-scales perturbation method as described in Kevorkian and Cole (Kevorkian and Cole, 1981) can be used effectively to construct asymptotic approximations of the solution on long timescales.
