  This paper describes an investigation of the early evolution of extragalactic
radio sources using samples of faint and bright Gigahertz Peaked Spectrum (GPS)
and Compact Steep Spectrum (CSS) radio galaxies. Correlations found between
their peak frequency, peak flux density and angular size provide strong
evidence that synchrotron self absorption is the cause of the spectral
turnovers, and indicate that young radio sources evolve in a self-similar way.
In addition, the data seem to suggest that the sources are in equipartition
while they evolve. If GPS sources evolve to large size radio sources, their
redshift dependent birth-functions should be the same. Therefore, since the
lifetimes of radio sources are thought to be short compared to the Hubble time,
the observed difference in redshift distribution between GPS and large size
sources must be due to a difference in slope of their luminosity functions. We
argue that this slope is strongly affected by the luminosity evolution of the
individual sources. A scenario for the luminosity evolution is proposed in
which GPS sources increase in luminosity and large scale radio sources decrease
in luminosity with time. This evolution scenario is expected for a ram-pressure
confined radio source in a surrounding medium with a King profile density. In
the inner parts of the King profile, the density of the medium is constant and
the radio source builds up its luminosity, but after it grows large enough the
density of th e surrounding medium declines and the luminosity of the radio
source decreases. A comparison of the local luminosity function (LLF) of GPS
galaxies with that of extended sources is a good test for this evolution
scenario [abridged].
