Delta and singular delta locus for one-dimensional systems of conservation laws

This work gives a condition for existence of singular and delta shock wave solutions to Riemann problem for 2×2 systems of conservation laws. For a fixed left‐hand side value of Riemann data, the condition obtained in the paper describes a set of possible right‐hand side values. The procedure is sim...

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Veröffentlicht in:	Mathematical methods in the applied sciences 2004-05, Vol.27 (8), p.931-955
1. Verfasser:	Nedeljkov, Marko
Format:	Artikel
Sprache:	eng
Schlagworte:	delta shock waves Exact sciences and technology generalized solutions Mathematical analysis Mathematics Sciences and techniques of general use singular shock waves systems of conservation laws
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	This work gives a condition for existence of singular and delta shock wave solutions to Riemann problem for 2×2 systems of conservation laws. For a fixed left‐hand side value of Riemann data, the condition obtained in the paper describes a set of possible right‐hand side values. The procedure is similar to the standard one of finding the Hugoniot locus. Fluxes of the considered systems are globally Lipschitz with respect to one of the dependent variables. The association in a Colombeau‐type algebra is used as a solution concept. Copyright © 2004 John Wiley &Sons, Ltd.
ISSN:	0170-4214 1099-1476
DOI:	10.1002/mma.480