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

Abstract

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.