The bifurcation analysis of the MHD Rankine–Hugoniot equations for a perfect gas

Freistühler, Heinrich; Rohde, Christian

The bifurcation analysis of the MHD Rankine–Hugoniot equations for a perfect gas

Dateien

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Datum

2003

Autor:innen

Freistühler, Heinrich

Rohde, Christian

DOI (zitierfähiger Link)

https://doi.org/10.1016/S0167-2789(03)00206-9

Sammlungen

Mathematik und Statistik

Publikationstyp

Zeitschriftenartikel

Publikationsstatus

Published

Erschienen in

Physica D : Nonlinear Phenomena. 2003, 185(2), pp. 78-96. ISSN 0167-2789. eISSN 1872-8022. Available under: doi: 10.1016/S0167-2789(03)00206-9

Zusammenfassung

This article provides a 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 also a prerequisite for new results on the existence and bifurcation of viscous profiles for intermediate MHD shock waves that are presented in a separate paper.

Fachgebiet (DDC)

510 Mathematik

Zitieren

ISO 690

FREISTÜHLER, Heinrich, Christian ROHDE, 2003. The bifurcation analysis of the MHD Rankine–Hugoniot equations for a perfect gas. In: Physica D : Nonlinear Phenomena. 2003, 185(2), pp. 78-96. ISSN 0167-2789. eISSN 1872-8022. Available under: doi: 10.1016/S0167-2789(03)00206-9

BibTex

@article{Freistuhler2003-11bifur-40833,
  year={2003},
  doi={10.1016/S0167-2789(03)00206-9},
  title={The bifurcation analysis of the MHD Rankine–Hugoniot equations for a perfect gas},
  number={2},
  volume={185},
  issn={0167-2789},
  journal={Physica D : Nonlinear Phenomena},
  pages={78--96},
  author={Freistühler, Heinrich and Rohde, Christian}
}

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