  Extending previous work with Lattanzio and Mascia on the scalar (in
fluid-dynamical variables) Hamer model for a radiative gas, we show nonlinear
orbital asymptotic stability of small-amplitude shock profiles of general
systems of coupled hyperbolic--eliptic equations of the type modeling a
radiative gas, that is, systems of conservation laws coupled with an elliptic
equation for the radiation flux, including in particular the standard
Euler--Poisson model for a radiating gas. The method is based on the derivation
of pointwise Green function bounds and description of the linearized solution
operator, with the main difficulty being the construction of the resolvent
kernel in the case of an eigenvalue system of equations of degenerate type.
Nonlinear stability then follows in standard fashion by linear estimates
derived from these pointwise bounds, combined with nonlinear-damping type
energy estimates
