@article {2007, title = {BV instability for the Lax-Friedrichs scheme}, number = {SISSA;100/2004/M}, year = {2007}, abstract = {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.}, url = {http://hdl.handle.net/1963/2335}, author = {Paolo Baiti and Alberto Bressan and Helge Kristian Jenssen} }