  A full symmetry classification is given for models of energy transport in
radiant plasma when the mass density is spatially variable and the diffusivity
is nonlinear. A systematic search for conservation laws also leads to some
potential symmetries, and to an integrable nonlinear model. Classical point
symmetries, potential symmetries and nonclassical symmetries are used to effect
variable reductions and exact solutions. The simplest time-dependent solution
is shown to be stable, and relevant to a closed system.
