  In low-density or high-temperature plasmas, Compton scattering is the
dominant process responsible for energy transport. Kompaneets in 1957 derived a
non-linear degenerate parabolic equation for the photon energy distribution. In
this paper we consider a simplified model obtained by neglecting diffusion of
the photon number density in a particular way. We obtain a non-linear
hyperbolic PDE with a position-dependent flux, which permits a one-parameter
family of stationary entropy solutions to exist. We completely describe the
long-time dynamics of each non-zero solution, showing that it approaches some
non-zero stationary solution. While the total number of photons is formally
conserved, if initially large enough it necessarily decreases after finite time
through an out-flux of photons with zero energy. This corresponds to formation
of a Bose-Einstein condensate, whose mass we show can only increase with time.
