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arXiv · 2211.07929

A note on separation conditions of resonance sets in the instability analysis for high-frequency oscillations in geometric optics

Jiaojiao Pan
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Abstract

In this paper, we study the instability of highly-oscillating solutions to semi-linear hyperbolic systems. A instability criterion was given in \cite{Lu} under rather strong separation conditions of resonance sets: coupled resonance sets are pairwise disjoint. Here we show that such separation conditions in \cite{Lu} can be relaxed: one of the coupled non-transparent resonance sets is allowed to intersect with at most two others. We obtain the same instability criterion as in \cite{Lu}. Finally, we give some applications to coupled Klein-Gordon systems with equal masses and nonlinear terms specified particularly, where on the intersections of resonance sets, the related interaction coefficients are non-transparent.

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Jiaojiao Pan. 2022-11-15. A note on separation conditions of resonance sets in the instability analysis for high-frequency oscillations in geometric optics. https://arxiv.org/abs/2211.07929

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