Low-Frequency Stability Analysis of Periodic Traveling-Wave Solutions of Viscous Conservation Laws in Several Dimensions
Low-Frequency Stability Analysis of Periodic Traveling-Wave Solutions of Viscous Conservation Laws in Several Dimensions
复制标题
多维粘性守恒定律周期行波解的低频稳定性分析
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
K. Zumbrun
中科院分区：
文献类型：
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作者：
Mh Oh;K. Zumbrun
我们概括了 Oh、Zumbrun 和 Serre 关于粘性守恒定律系统的空间周期行波谱稳定性的工作，从一维到多维设置。具体来说，我们将 Serre 观察到的关于波的线性化方程在零频率附近的线性化色散关系与通过慢调制（WKB）近似获得的均匀化系统之间的联系扩展到多维。这可以被视为 WKB 扩展的部分理由；直接的结果是多维均质系统的双曲性是波稳定性的必要条件。正如 Oh 和 Zumbrun 在一维中所指出的，低频色散关系的描述也是确定时间渐近行为的第一步。
We generalize work of Oh & Zumbrun and Serre on spectral stability of spatially periodic traveling waves of systems of viscous conservation laws from the one-dimensional to the multi-dimensional setting. Specifically, we extend to multi-dimensions the connection observed by Serre between the linearized dispersion relation near zero fre- quency of the linearized equations about the wave and the homogenized system obtained by slow modulation (WKB) approximation. This may be regarded as partial justification of the WKB expansion; an immediate consequence is that hyperbolicity of the multi-dimensional homogenized system is a necessary condition for stability of the wave. As pointed out by Oh & Zumbrun in one dimension, description of the low-frequency dispersion relation is also a first step in the determination of time-asymptotic behavior.