DefinePK

Abstract

In this study 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 how a multiple time-scales perturbation method can be used effectively to construct asymptotic approximations of the solution on long timescales. The main problem of this paper is to study how efficiently these boundary dampers work.