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.
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Audebert, B., Coquel, F. (2008). Structural Stability of Shock Solutions of Hyperbolic Systems in Nonconservation Form via Kinetic Relations. In: Benzoni-Gavage, S., Serre, D. (eds) Hyperbolic Problems: Theory, Numerics, Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75712-2_36
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