Stability of Conservation Laws with Discontinuous Coefficients

Stability of Conservation Laws with Discontinuous Coefficients

We prove L1 contractivity of weak solutions to a conservation law with a flux function that may depend discontinuously on the space variable. Furthermore, we show that the L1 difference between solutions to conservation laws with different flux functions is bounded by the total variation with respec...

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Veröffentlicht in:Journal of Differential Equations 1999-09, Vol.157 (1), p.41-60
Hauptverfasser: Klausen, Runhild Aae, Risebro, Nils Henrik
Format: Artikel
Sprache:eng
Schlagworte:
conservation laws
non-strictly hyperbolic
stability
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Zusammenfassung:We prove L1 contractivity of weak solutions to a conservation law with a flux function that may depend discontinuously on the space variable. Furthermore, we show that the L1 difference between solutions to conservation laws with different flux functions is bounded by the total variation with respect to the space variable, of the difference between the flux functions.
ISSN:0022-0396
1090-2732
DOI:10.1006/jdeq.1998.3624