小冲击的Lopatinski行列式可能消失
The Lopatinski determinant of small shocks may vanish
摘要：
Kreiss-Majda Lopatinski行列式描述了多空间变量双曲守恒律方程组激波解的一致稳定性。本文讨论振幅足够小的激波的Lopatinski行列式。已知对于所谓的极端冲击波，即，行列式是非零的。例如，如果模式是Metivier凸的，则冲击波与系统在给定传播方向上显示的最慢或最快模式相关联。本文的结果是，对于任意小的非极值激波与Metivier凸模式，洛帕特列行列式可能为零。
英文摘要：
The Kreiss-Majda Lopatinski determinant encodes a uniform stability property of shock wave solutions to hyperbolic systems of conservation laws in several space variables. This note deals with the Lopatinski determinant for shock waves of sufficiently small amplitude. The determinant is known to be non-zero for so-called extreme shock waves, i. e., shock waves which are asscoiated with either the slowest or the fastest mode the system displays for a given direction of propagation, if the mode is Metivier convex. The result of the note is that for arbitrarily small non-extreme shock waves associated with a Metivier convex mode, the Lopatsinki determinant may vanish.
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