Singular shock waves in interactions

Abstract

In a number of papers it has been shown that there exist one-dimensional systems such that they contain solutions with so-called overcompressive singular shock waves besides the usual elementary waves (shock and rarefaction waves as well as contact discontinuities). One can see thei r definition for a general 2 × 2 system with fluxes linear in one of the dependent variables in Nedeljkov, Delta and singular delta locus for one dimensional systems of conservation laws, Math. Method Appl. Sci. 27 (2004), 931-955. This paper is devoted to examining their interactions with themselves and elementary waves. After a discussion of systems given in a general form, a complete analysis will be given for the ion-acoustic system given in Keyfitz and Kranzer, Spaces of weighted measures for conservation laws with singular shock solutions, J. Differ. Equations 118 (1995), no. 2, 420-451. © 2008 Brown University.