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Riemann Problem for Conservation Laws with an Umbilic Point

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Book cover Hyperbolic Problems: Theory, Numerics, Applications

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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.

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Author information

Authors and Affiliations

  1. Faculty of Engineering, Osaka Electro-Communication Univ, Japan

    Fumioki Asakura

  2. Institute of Mathematics, Univ. of Tsukuba, Japan

    Mitsuru Yamazaki

Authors
  1. Fumioki Asakura
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  2. Mitsuru Yamazaki
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Editor information

Editors and Affiliations

  1. Department of Applied and Computational Mathematics 217-50, California Institute of Technology, Pasadena, CA, 91125, USA

    Thomas Y. Hou

  2. Center for Scientific Computation and Mathematical Modeling (CSCAMM) Department of Mathematics, University of Maryland, College Park, MD, 20742-3289, USA

    Eitan Tadmor

  3. Institute for Physical Science & Technology (IPST), University of Maryland, College Park, MD, 20742-3289, USA

    Eitan Tadmor

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© 2003 Springer-Verlag Berlin Heidelberg

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Asakura, F., Yamazaki, M. (2003). Riemann Problem for Conservation Laws with an Umbilic Point. In: Hou, T.Y., Tadmor, E. (eds) Hyperbolic Problems: Theory, Numerics, Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55711-8_28

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  • DOI: https://doi.org/10.1007/978-3-642-55711-8_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-62929-7

  • Online ISBN: 978-3-642-55711-8

  • eBook Packages: Springer Book Archive

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