This work is concerned with shock waves in a magnetohydrodynamic (MHD) system for a single fluid, and in a system for anisotropic plasmas. The ideal MHD equations are non-strictly hyperbolic and non-convex. Intermediate shocks (which may be over-compressive) can exist and Riemann solutions may not be unique. Results based on dissipative MHD equations show that the evolution and shock structure are related. There are two pressures in anisotropic plasma, one parallel to the magnetic field and one perpendicular to the magnetic field; the number of variables is increased by one from the MHD system and so is the number of small amplitude waves. In addition, unlike the MHD system, the speed of an intermediate wave does not necessarily lie between the speeds of the fast and slow waves. Some of the complexity of the wave structure and the Riemann solution in anisotropic plasma will be demonstrated by numerical examples.
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