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Riemann Problem for Conservation Laws with an Umbilic Point

In: Hyperbolic Problems: Theory, Numerics, Applications

Author

Listed:
  • Fumioki Asakura

    (Osaka Electro-Communication Univ, Faculty of Engineering)

  • Mitsuru Yamazaki

    (Univ. of Tsukuba, Institute of Mathematics)

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.

Suggested Citation

  • Fumioki Asakura & Mitsuru Yamazaki, 2003. "Riemann Problem for Conservation Laws with an Umbilic Point," Springer Books, in: Thomas Y. Hou & Eitan Tadmor (ed.), Hyperbolic Problems: Theory, Numerics, Applications, pages 315-323, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-55711-8_28
    DOI: 10.1007/978-3-642-55711-8_28
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