  A model for the evolution of low-luminosity radio galaxies is presented. In
the model, the lobes inflated by low-power jets are assumed to expand in near
pressure-balance against the external medium. Both cases of constant external
pressure and decreasing external pressure are considered. Evolution of an
individual source is described by the power-size track. The source appears as
its lobe is inflated and radio luminosity increases to above the detection
level; the source then moves along the track and eventually disappears as its
luminosity drops below the detection limit. The power-size tracks are
calculated including the combined energy losses due to synchrotron radiation,
adiabatic expansion, and inverse Compton scattering. It is shown that in
general, the constant-pressure model predicts an excess number of luminous,
small-size sources while underpredicting large-size sources in the power-size
diagram. The predicted spectra are steep for most sources, which is
inconsistent with observations. By comparison, the pressure-limiting model fits
observations better. In this model, low-luminosity sources undergo substantial
expansion losses in the initial phase and as a result, it predicts fewer
luminous, small-size sources. The resultant spectra are flat for most sources
except for the oldest ones, which seems consistent with observations. The
power-size tracks, in contrast to that of high-luminosity radio galaxies, are
characterized by a slow increase in luminosity for most of the source's life,
followed by a rapid decline when the synchrotron or inverse Compton scattering
losses set in.
