  The strong optical flash observed by ROTSE, as well as the radio flare
associated with GRB 990123 can be attributed to the emission of the fireball
ejecta, initially heated by the reverse shock. We numerically study the
evolution of an adiabatic relativistic fireball interacting with an ambient
uniform medium, both in the initial energy transfer stage and in its late
evolution. It is shown that the Blandford-McKee solution adequately describes
the evolution of the shocked shell quite early on and for as long as the
fireball material has relativistic temperatures. In the case where the reverse
shock is only mildly relativistic the shocked shell becomes cold almost
immediately and the evolution deviates from the Blandford-McKee solution. We
derive analytical expressions for the ejecta evolution in its cold regime. This
solution gives a good approximation to the numerical results. We estimate the
radiation from the fireball ejecta using the numerical hydrodynamic evolution
in both cases: cold and hot shells. Surprisingly, we find that both evolutions
give rather similar light curves, decaying approximately as $T^{-2}$ in the
optical and peaking at about one day in the radio, even though the
hydrodynamics is different.
