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Strong oscillations on a linearly degenerate field. (Oscillations fortes sur un champ linéairement dégénéré.) (French. English summary) Zbl 1091.35039

Summary: Transparencies happen for quasilinear waves associated to linearly degenerate eigenvalues, leading to linear geometric optics. To reach nonlinear phenomena, we have to consider larger amplitudes. We show that approximate solutions can still be constructed. We find intrinsic conditions allowing to justify the approximation. In the absence of these conditions, instabilities are created. We analyse the different types of the underlying instabilities.

MSC:

35L65 Hyperbolic conservation laws
35Q60 PDEs in connection with optics and electromagnetic theory
35F20 Nonlinear first-order PDEs
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