Baiti, PaoloBressan, AlbertoJenssen, Helge Kristian2007-11-052011-09-072007-11-052011-09-072007-11-05https://openscience.sissa.it/handle/1963/2335It 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.257155 bytesapplication/pdfen-USPreprint