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Instability of travelling wave profiles for the Lax-Friedrichs scheme

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  • 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 $n$.
    Mathematics Subject Classification: 35L65, 35B05.

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