... 1, March 2008 (? 2007) DOI: 10.1007/s10884-007-9070-5 Hyperbolicity singularities in Rarefaction Waves Alexei A. Mailybaev 1,3 and Dan Marchesin 2 Received March 7, 2005; Revised March 20, 2006 For mixed-type systems of conservation laws, rarefaction waves may contain states at the boundary of the elliptic region, where two characteristic speeds coincide, and the Lax family of the wave changes. ... In these models, rarefaction curves typically contain a point at the boundary of the elliptic region. ...