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Global oscillatory waves for second order quasilinear wave equations

par Godin, Paul
Référence Transactions of the American Mathematical Society, 346, 2, page (523-547)
Publication Publié, 1994

Article révisé par les pairs

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Résumé :

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. 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. © 1994 American Mathematical Society.