AN ASYMPTOTIC THEORY FOR A CLASS OF INITIAL-BOUNDARY VALUE-PROBLEMS FOR WEAKLY NONLINEAR-WAVE EQUATIONS WITH AN APPLICATION TO A MODEL OF THE GALLOPING OSCILLATIONS OF OVERHEAD TRANSMISSION-LINES

An asymptotic theory for a class of initial-boundary value problems for weakly nonlinear wave equations is presented. The theory implies the well-posedness of the problem in the classical sense and the validity of formal approximations on long timescales. As an application of the theory, an initial-boundary value problem for a Rayleigh wave equation is studied in detail using a two-timescale perturbation method. From an aeroelastic analysis, it is shown that this initial-boundary value problem may be regarded as a model describing the growth of wind-induced oscillations of overhead transmission lines.