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Admissibility of Shock Waves and Uniqueness of the Riemann Problem

In: Hyperbolic Problems: Theory, Numerics, Applications

Author

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  • Fumioki Asakura

    (Osaka Electro-Communication Univ, Faculty of Eugineering)

Abstract

We study the admissibility of shock waves and the uniqueness of the Riemann problem for a general 2 × 2 hyperbolic system of conservation laws in one space dimension: U t + F(U) x =0 with initial data having large amplitude. We assume that that the characteristic fields are strictly separated; that is: there exist two disjoint (open) conical neighborhoods such that the first characteristic field is confined to one of these neighborhoods and the second characteristic field to the other. We show that, together with some technical assumptions, the viscous profile exists for states U−, U+ not necessarily close and there exists at most one solution to the Riemann problem. These results will generalize admissibility and uniqueness theorems of Liu and Smoller, by giving descriptions free from particular choice of rectangular coordinates.

Suggested Citation

  • Fumioki Asakura, 2003. "Admissibility of Shock Waves and Uniqueness of the Riemann Problem," Springer Books, in: Thomas Y. Hou & Eitan Tadmor (ed.), Hyperbolic Problems: Theory, Numerics, Applications, pages 325-334, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-55711-8_29
    DOI: 10.1007/978-3-642-55711-8_29
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