Abstract
In this paper we prove the global existence and describe the asymptotic behaviour of a family of oscillatory solutions of Cauchy problems for a class of scalar second order quasilinear wave equations, when the space dimension is odd and at least equal to 3 3 . If time is bounded, corresponding results for quasilinear first order systems were obtained by Guès; to prove our results we reduce our problems to bounded time problems with the help of a conformal inversion. To obtain global results, suitable geometric assumptions must be made on the set where the oscillations are concentrated at initial time.
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