Small, medium and large shock waves for non-equilibrium radiation hydrodynamic

We examine the existence of shock profiles for a hyperbolic-elliptic system arising in radiation hydrodynamics. The algebraic-differential system for the wave profile is reduced to a standard two-dimensional form that is analyzed in details showing the existence of heteroclinic connection between the two singular points of the system for any distance between the corresponding asymptotic states of the original model. Depending on the location of these asymptotic states, the profile can be either continuous or possesses at most one point of discontinuity. Moreover, a sharp threshold relative to presence of an internal absolute maximum in the temperature profile --also called {\sf Zel'dovich spike}-- is rigourously derived.