Lax-Friedrichs格式的BV不稳定性
BV instability for the Lax-Friedrichs scheme
摘要：
证明了守恒律组的Lax-Friedrichs格式的离散激波剖面（DSP）在BV中不一定连续地依赖于它们的速度。我们构建的$2 \times 2$系统的例子，其中有一系列的DSP的速度收敛到一个有理数。由于谐振现象，限制DSP和序列中的任何DSP之间的差异将包含一阶变化量。
英文摘要：
It is proved that discrete shock profiles (DSPs) for the Lax-Friedrichs scheme for a system of conservation laws do not necessarily depend continuously in BV on their speed. We construct examples of $2 \times 2$-systems for which there are sequences of DSPs with speeds converging to a rational number. Due to a resonance phenomenon, the difference between the limiting DSP and any DSP in the sequence will contain an order-one amount of variation.
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