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The Bifurcation Analysis of the MHD Rankine-Hugoniot Equations for a Perfect Gas
Heinrich Freistühler and Christian Rohde
This article provides the complete bifurcation analysis of the Rankine-Hugoniot equations for compressible magnetohydrodynamics (MHD) in the case of a perfect gas. Particular scaling properties of the perfect-gas equation of state are used to reduce the number of bifurcation parameters. The smaller number, together with a novel choice, of these parameters results in a detailed picture of the global situation which is distinctly sharper than the one implied by previous literature.
The description includes statements about the location, topology, and dimensions of various regimes, corresponding to different combinations of possible shock waves of given type, in dependence of the adiabatic exponent of the gas.
The analysis is a crucial step for our detailed study of existence and bifurcation of viscous profiles for intermediate MHD shock waves that will be presented in a separate paper.