Darmawijoyo, Darmawijoyo and Van Horssen, W.T. (2002) *On A Characteristic Layer Problem For A Weakly Damped String.* Reports of the Department of Applied Mathematical Analysis. ISSN 1389-6520

## Abstract

In this paper initial-boundary value problems for a string (a 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 dashpot system, where the damping generated by the dashpot system is assumed to be small, and is assumed to be proportional to the vertical and the angular velocity of the string in the endpoint. This problem can be regarded as a rather simple model describing oscillations of exible structures such as for instance overhead power transmission lines. A semigroup approach will be used to prove the wellposedness of the singularly perturbed problem. It will be shown how a multiple scales perturbation method can be used effectively to construct asymptotic approximations of the solution on long timescales. Based on these asymptotic results the effectiveness of the dashpot system is discussed.

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