Preprint 2004-039

Paolo Baiti, Alberto Bressan and Helge Kristian Jenssen

Instability of Travelling Wave Profiles for the Lax–Friedrichs scheme

Abstract: We study travelling wave profiles for discrete approximations to hyperbolic systems of conservation laws. A detailed example is constructed, showing that for the Lax–Friedrichs scheme the travelling profiles do not depend continuously on the wave speed, in the BV norm. Namely, taking a sequence of wave speeds λn→λ, the corresponding profiles Ψn converge to a limit Ψ uniformly on the real line, but Tot.Var.{Ψn-Ψ}≥c0>0 for all n.

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Paolo Baiti, <>
Alberto Bressan, <>
Helge Kristian Jenssen, <>
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<> July 22 2004.

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