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Structural Stability of Shock Solutions of Hyperbolic Systems in Nonconservation Form via Kinetic Relations

In: Hyperbolic Problems: Theory, Numerics, Applications

Author

Listed:
  • B. Audebert

    (Office National d'Etudes et Recherches Aérospatiales)

  • F. Coquel

    (Université Pierre et Marie Curie, CNRS et Laboratoire Jacques Louis Lions)

Abstract

We introduce stability conditions for shock solutions of hyperbolic systems in nonconservation form. The recently proposed framework of kinetic relations for defining shock solutions is shown to yield a natural extension of the structural stability conditions due to Majda in the conservative setting: besides the mandatory geometric Lax conditions, a direct extension of the Majda determinant must not vanish. We study these conditions for validity within the frame of PDE systems for modelling shock-turbulence interactions. We prove that a mostly neglected nonconservative correction to the PDEs plays a major role in the stability.

Suggested Citation

  • B. Audebert & F. Coquel, 2008. "Structural Stability of Shock Solutions of Hyperbolic Systems in Nonconservation Form via Kinetic Relations," Springer Books, in: Sylvie Benzoni-Gavage & Denis Serre (ed.), Hyperbolic Problems: Theory, Numerics, Applications, pages 397-405, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-75712-2_36
    DOI: 10.1007/978-3-540-75712-2_36
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