论文标题
关于在几何光学器件中高频振荡的不稳定性分析中共振集的分离条件的注释
A note on separation conditions of resonance sets in the instability analysis for high-frequency oscillations in geometric optics
论文作者
论文摘要
在本文中，我们研究了半线性双曲系统的高度振荡溶液的不稳定性。在\ cite {lu}中给出了不稳定性标准，在共振集的相当强的分离条件下：耦合共振集是成对的脱节。在这里，我们表明\ cite {lu}中的这种分离条件可以放松：允许最多两种耦合的非透明共振集与其他两个耦合共振集相交。我们获得与\ cite {lu}中相同的不稳定性标准。最后，我们将一些应用程序提供给具有相同质量和非线性术语的耦合的klein-gordon系统，特别是在共振集的相交的情况下，相关的相互作用系数是非透明的。
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.
