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Transactions of the American Mathematical Society

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Global oscillatory waves for second order quasilinear wave equations

Author: Paul Godin
Journal: Trans. Amer. Math. Soc. 346 (1994), 523-547
MSC: Primary 35L70; Secondary 35B40, 58G16
MathSciNet review: 1270662
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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$. 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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Keywords: Quasilinear second order wave equations, global existence, oscillatory solutions, conformal inversion
Article copyright: © Copyright 1994 American Mathematical Society