Abstract
We illustrate, in the framework of magnetohydrodynamics, an application of crossing shock formulas to a characteristic shock moving perpendicularly to the magnetic field.
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S. K. GODUNOV, An interesting class of quasi-linear systems.Sov. Math. 2, 947 (1961); Symmetric form of the magnetohydrodynamic equations (in Russian). Preprint,Akad. Nauk. SSSR Sib. Otd., Vychisl. Tsentr 3, No. 1, 26 (1972)
K. O. FRIEDRICHS, P. D. LAX, Systems of conservation equations with a convex extension,Proc. Nat. Acad. Sci. U.S.A. 68, 1686 (1971)
T. RUGGERI, A. STRUMì A, Main field and convex covariant density for quasi linear hyperbolic systems,Ann. Inst. Henri Poincaré 34, 65 (1981)
A. M. ANILE, S. PENNISI, On the mathematical structure of the relativistic magneto-fluid dynamics.Ann. Inst. Henri Poincaré 46, 27 (1987)
A. M.A ANILE,Relativistic fluids and magneto-fluids. Cambridge Monographs on Mathematical Physics, Cambridge University Press (1989)
I. MÜLLER, T. RUGGERI,Extended Thermodynamics. Springer-Verlag New York, Berlin (1993)
G. BOILLAT, S. PLUCHINO, Sopra l'iperbolicità dei sistemi con vincoli e considerazioni sul superfluido e la magnetoidrodinamica,ZAMP 36, 893 (1985)
G. BOILLAT, Sur l'existence et la recherche d' équations de conservation supplémentaires pour les systèmes hyperboliques.C. R. Acad. Sci. Paris 278, série A, 909 (1974); Symétrisation des systèmes d' équations aux derivées partielles avec densité d' énergie convexe et contraintes. Ibid.295, série I, 551 (1982)
G. BOILLAT, Involutions des systèmes conservatifs,C. R. Acad. Sci. Paris,307, série I, 891 (1988)
P. D. LAX, The multiplicity of eigenvalues,Bull. Amer. Math. Soc. 6, 213 (1982)
S. FRIEDLAND, J. W. ROBBIN, J. H. SYLVESTER, On the crossing rule,Comm. Pure. Appl. Math. 37, 19 (1984)
G. BOILLAT, A. MURACCHINI, Chocs caractéristiques de croisement.C. R. Acad. Sci. Paris 310, série I, 229 (1990)
G. BOILLAT, Expression explicite des chocs caractéristiques de croisement,C.R. Acad. Sci. Paris 312, série I, 653 (1991)
A. JEFFREY,Magnetohydrodynamics, Oliver and Boyd, London (1966)
H. CABANNES,Theoretical Magnetofluiddynamics. Academic Press, New York (1970)
G. BOILLAT, A. MURACCHINI, The structure of the characteristic shocks in constrained symmetric systems with application to magnetohydrodynamics,Wave Motion 11, 297 (1989)
A. LICHNEROWICZ,Relativistic hydrodynamics and magnetohydrodynamics. Benjamin, New York (1967); Ondes de chocs, ondes infinitésimales et rayons en hydrodynamique et magnétohydrodynamique relativistes, in:Relativistic Fluid Dynamics, Ed. C. Cattaneo, Cremonese, Roma (1971)
G. BOILLAT, T. RUGGERI, Wave and shock velocities in relativistic magnetohydrodynamics compared with the speed of light,Continuum Mech. Thermodyn. 1, 47 (1989)
S. PENNISI, A covariant and extended model for relativistic magnetofluiddynamics,Ann. Inst. Henri Poincaré,58, 343 (1993)
G. BOILLAT, Sur l'élimination des contraintes involutives,C.R. Acad. Sci. Paris 318, série I, 1053 (1994)
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Supported by C.N.R. (G.N.F.M.) and MURST (Fondi Ricerche 40% and 60%)
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Boiliat, G., Muracchini, A. Characteristic shocks of crossing velocities in magnetohydrodynamics. NoDEA 3, 217–230 (1996). https://doi.org/10.1007/BF01195915
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DOI: https://doi.org/10.1007/BF01195915