Instability of travelling wave profiles for the Lax-Friedrichs scheme | Zendy

Paolo Baiti | Zendy; Alberto Bressan | Zendy; Helge Kristian Jenssen | Zendy

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Instability of travelling wave profiles for the Lax-Friedrichs scheme

Author(s) -

Paolo Baiti,

Alberto Bressan,

Helge Kristian Jenssen

Publication year - 2005

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2005.13.877

Subject(s) - traveling wave , conservation law , lambda , limit (mathematics) , norm (philosophy) , physics , instability , mathematical analysis , scheme (mathematics) , mathematics , mathematical physics , mechanics , quantum mechanics , law , political science

We study travelling wave profiles for discrete approximations to hyper- bolic 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 n ! , the corresponding profiles n converge to a limit uniformly on the real line, but Tot.Var.{ n } c0 > 0 for all n.

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