Hyperbolicity singularities in rarefaction waves
Alexei Mailybaev | Marchesin, Dan
systems of conservation laws | type change | rarefaction waves | Riemann solutions | classifications of singularities | versal deformation
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. Such contiguous rarefaction waves form a single fan with a continuous profile. Different pairs of families may appear in such rarefactions, giving rise to novel Riemann solution structures. We study the structure of such rarefaction waves near regular and exceptional points of the elliptic boundary and describe their effect on Riemann solutions.