BV instability for the Lax-Friedrichs scheme

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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 $2 \times 2$-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.
24 pages, 3 figures

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Analysis of PDEs

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http://salesiana.dossiersoluciones.com/handle/123456789/74048

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0502043
 http://arxiv.org/abs/math/0502043

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arXiv