BV instability for the Lax-Friedrichs scheme
Analysis of PDEs
2007-05-23 v1
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 -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.
Cite
@article{arxiv.math/0502043,
title = {BV instability for the Lax-Friedrichs scheme},
author = {Paolo Baiti and Alberto Bressan and Helge Kristian Jenssen},
journal= {arXiv preprint arXiv:math/0502043},
year = {2007}
}
Comments
24 pages, 3 figures