Riemann Problem for Conservation Laws with an Umbilic Point

Fumioki Asakura () and Mitsuru Yamazaki ()
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Fumioki Asakura: Osaka Electro-Communication Univ, Faculty of Engineering
Mitsuru Yamazaki: Univ. of Tsukuba, Institute of Mathematics

A chapter in Hyperbolic Problems: Theory, Numerics, Applications, 2003, pp 315-323 from Springer

Abstract: Abstract We study the Riemann problems for 2 × 2 conservation laws with a hyperbolic singularity. The flux are a pair of quadratic functions where the char acteristic speeds are equals and the Jacobian matrix is diagonal at the hyperbolic singularity i.e. umbilic point. Discontinuous solutions will be considered. They are characterized by 2 points on the Hugoniot curves which consist of 1-Hugoniot curve, 2-Hugoniot curve and a detached curve. The parts of compressible and overcompressible waves on the wave curves will be determined.

Keywords: Shock Wave; Riemann Problem; Umbilic Point; Hugoniot Curve; Wave Curve (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-55711-8_28

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DOI: 10.1007/978-3-642-55711-8_28

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