English

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 2×22 \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.

Keywords

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