%0 Journal Article
%T BV instability for the Lax-Friedrichs scheme
%A Paolo Baiti
%A Alberto Bressan
%A Helge Kristian Jenssen
%J Mathematics
%D 2005
%I arXiv
%X 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.
%U http://arxiv.org/abs/math/0502043v1