July  2005, 13(4): 877-899. doi: 10.3934/dcds.2005.13.877

Instability of travelling wave profiles for the Lax-Friedrichs scheme

1. 

Dipartimento di Matematica e Informatica, Università di Udine, Via delle Scienze 206, Udine 33100

2. 

Department of Mathematics, Penn State University, University Park, Pa.16802, United States

3. 

Department of Mathematics, North Carolina State University, Raleigh, NC 27695, United States

Received  August 2004 Revised  February 2005 Published  August 2005

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 $\lambda_n\to\lambda$, the corresponding profiles $\Psi_n$ converge to a limit $\Psi$ uniformly on the real line, but Tot.Var.{$\Psi_n-\Psi$}$\geq c_0>0$ for all $n$.
Citation: Paolo Baiti, Alberto Bressan, Helge Kristian Jenssen. Instability of travelling wave profiles for the Lax-Friedrichs scheme. Discrete & Continuous Dynamical Systems - A, 2005, 13 (4) : 877-899. doi: 10.3934/dcds.2005.13.877
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