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 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.
Keywordssystems of conservation laws type change rarefaction waves Riemann solutions classification of singularities versal deformation
Unable to display preview. Download preview PDF.
- 3.Azevedo, A. V., and Marchesin, D. (1990). Multiple viscous profile Riemann solutions in mixed elliptic-hyperbolic models for flow in porous media. In Nonlinear Evolution Equations that Change Type, IMA Vol. Math. Appl. 27, Springer, New York.Google Scholar
- 15.Marchesin D. and Plohr B. (2001). Wave structure in WAG recovery. Soc. Petroleum Eng. J, 6: 209–219 Google Scholar
- 16.Matos, V. M. M. (2004). Riemann Problem for Two Conservation Laws of Type IV with Elliptic Region, Ph.D. Thesis, IMPA, Riode Janeiro (in Portuguese).Google Scholar
- 17.Palmeira, C. F. B. (1988). Line fields defined by eigenspaces of derivatives of maps from the plane to itself, Proceedings of the Sixth International Colloquium on Differential Geometry (Santiago de Compostela), pp 177–205.Google Scholar
- 19.Radicchi, R. (2005). On implicit ordinary differential equations in three dimensions, Ph.D Thesis, Universidade Federal de Minas Gerais, Minas Gerais (Brazil).Google Scholar
- 23.Schulte W. and Falls A. (1992). Features of three-component, three-phase displacement in porous media. SPE Reservoir Eng. 7: 426–432 Google Scholar