  We present radio observations of the afterglow of the bright gamma-ray burst
GRB 991208 at frequencies of 1.4, 4.9 and 8.5 GHz, taken between two weeks and
300 days after the burst. The well-sampled radio light curve at 8.5 GHz shows
that the peak flux density peaked about 10 days after the burst and decayed
thereafter as a power-law t^-1.07. This decay rate is more shallow than the
optical afterglow with t^-2.2, which was measured during the first week. These
late-time data are combined with extensive optical, millimeter and centimeter
measurements and fitted to the standard relativistic blast wave model. In
agreement with previous findings, we find that an isotropic explosion in a
constant density or wind-blown medium cannot explain these broadband data
without modifying the assumption of a single power-law slope for the electron
energy distribution. A jet-like expansion provides a reasonable fit to the
data. In this case, the flatter radio light curve compared to the optical may
be due to emission from an underlying host galaxy, or due to the blastwave
making a transition to non-relativistic expansion. The model that best
represents the data is a free-form model in which it is assumed that the
broadband emission originates from a synchrotron spectrum, while the
time-evolution of the break frequencies and peak flux density are solved for
explicitly. Although the decay indices for most of the synchrotron parameters
are similar to the jet model, the evolution of the cooling break is unusually
rapid, and therefore requires some non-standard evolution in the shock.
(abridged)
