Shock structure for heat conducting and viscid fluids

The shock structure problem is investigated for a class of theories offering relativistic generalizations developed by Muller (1966), which showed that a regular shock structure may exist only at low Mach numbers. Balance equations for a continuum are defined for a plane steady shock, and evolution equations are presented. Conditions are found within which the system of wave propagation is hyperbolic, and the structure of a steady plane shock wave is explored analytically. An asymptotic theory for weak shocks is studied, yielding a form which is independent of the form of the transport coefficients. A critical Mach number is obtained which limits the shock speed which will yield a stable structure, and the Muller equations in the stable regime are demonstrated to be equivalent to the Navier-Stokes-Fourier theory for the same speeds.