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- W1023157 abstract "The term of wave is used in a general way to name any solution of a hyperbolic problem () 0 Lu = , and the method used is a generalization of a geometrical process of optics (W.K.B.) consisting in seeking the solution in the form g ( attenuating factors). We thus build such an asymptotic solution in the cases of simple and multiple characteristics, provided that the Cauchy data has an asymptotic expansion, and observe, like other authors, that the phase function is a solution of the classical eikonal equation, and the terms of the series are determined by a recursive system of differential equations. We then deduce a condition for genuine non linearity of the problem which generalizes that of Lax (7) and John (3), and highlight from it the singular behaviour of the first term of the formal solution when the characteristics are distinct. We note that, for sufficiently small frequency, the asymptotic solution is almost global." @default.
- W1023157 created "2016-06-24" @default.
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- W1023157 date "2009-01-01" @default.
- W1023157 modified "2023-09-26" @default.
- W1023157 title "Asymptotic Waves for a Non Linear System" @default.
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