Darmawijoyo, Darmawijoyo (2003) *On a Rayleigh Wave Equation with Boundary Damping.* Reports of the Department of Applied Mathematical Analysis. ISSN 1389-6520

## Abstract

In this paper an initial-boundary value problem for a weakly nonlinear string (or wave) equation with non-classical boundary conditions is considered. One end of the string is assumed to be �xed and the other end of the string is attached to a 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 exible structures such as overhead transmission lines in a wind�eld. An asymptotic theory for a class of initial-boundary value problems for nonlinear wave equations is presented. It will be shown that the problems considered are well-posed for all time t. A multiple time-scales perturbation method in combination with the method of characteristics will be used to construct asymptotic approximations of the solution. It will also be shown that all solutions tend to zero for a sufficiently large value of the damping parameter. For smaller values of the damping parameter it will be shown how the string-system eventually will oscillate. Some numerical results are also presented in this paper.

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