Multidimensional Stability of Planar Viscous Shock Waves
Multidimensional Stability of Planar Viscous Shock Waves
复制标题
平面粘性冲击波的多维稳定性
DOI：
10.1007/978-1-4612-0193-9_5
复制
发表时间：
2001
影响因子：
2.4
通讯作者：
K. Zumbrun
中科院分区：
文献类型：
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作者：
K. Zumbrun
物理和数学上的考虑保证了在研究冲击波的稳定性，特别是在MHD，燃烧和多相流中，包括正则化效应，如扩散，耗散和/或松弛。实际上，在这种普遍性中，“理想激波”近似只在长波极限中有意义，也就是说，在大尺度中，而不是在小尺度中。同样，从实验和对无粘（双曲线）情况的研究中，已知多维效应在确定稳定性方面起关键作用。然而，直到最近，还没有对同时考虑这两种影响的系统进行严格的分析。
Physical and mathematical considerations warrant the inclusion of regularizing effects such as diffusion, dissipation, and/or relaxation in the study of stability of shock waves, particularly in MHD, combustion, and multiphase flow. Indeed, in this generality, the “ideal shock” approximation has relevance only in the long-wave limit, that is, in the large, but not in the small scale. Likewise, multidimensional effects are known both from experiment and from the study of the inviscid (hyperbolic) case to play a key role in determining stability. Yet, until very recently, there were no rigorous analyses for systems taking into account both effects simultaneously.