Hyperbolicity singularities in Rarefaction Waves

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 o...

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Bibliographic Details
Published in:	Journal of dynamics and differential equations Vol. 20; no. 1; pp. 1 - 29
Main Authors:	Mailybaev, Alexei A., Marchesin, Dan
Format:	Journal Article
Language:	English
Published:	Boston Springer US 01-03-2008
Subjects:	Applications of Mathematics Mathematics Mathematics and Statistics Ordinary Differential Equations Partial Differential Equations classification of singularities Riemann solutions type change systems of conservation laws versal deformation rarefaction waves
Online Access:	Get full text
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Summary:	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.
ISSN:	1040-7294 1572-9222
DOI:	10.1007/s10884-007-9070-5