The structure of MFD shock waves for rectilinear motion in some models of plasma

Hesaaraki, Mahmoud

doi:10.1090/S0002-9947-1995-1297528-4

The structure of MFD shock waves for rectilinear motion in some models of plasma

Author: Mahmoud Hesaaraki
Journal: Trans. Amer. Math. Soc. 347 (1995), 3423-3452
MSC: Primary 35L67; Secondary 34C99, 35Q35, 76L05, 76W05
DOI: https://doi.org/10.1090/S0002-9947-1995-1297528-4
MathSciNet review: 1297528
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Abstract: The mathematical question of the existence of structure for "fast", "slow" and "intermediate" MFD shock waves in the case of rectilinear motion in some model of plasma is stated in terms of a six-dimensional system of ordinary differential equations, which depends on five viscosity parameters. In this article we shall show that this system is gradient-like. Then by using the Conley theory we prove that the fast and the slow shocks always possess structure. Moreover, the intermediate shocks do not admit structure. Some limiting cases for singular viscosities are investigated. In particular, we show how the general results in the classical one fluid MHD theory are obtained when "the plasma viscosities" $\beta$ and $\chi$ tend to zero.

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