  Forward shocks caused by the interaction between a relativistic blast wave
and the circum-burst medium are thought to be responsible for the afterglow
emission in Gamma-Ray Bursts (GRBs). We consider the hydrodynamics of a
spherical relativistic blast wave expanding into the surrounding medium and we
generalize the standard theory in order to account for several effects that are
generally ignored. In particular, we consider the role of adiabatic and
radiative losses on the hydrodynamical evolution of the shock, under the
assumption that the cooling losses are fast. Our model can describe adiabatic,
fully radiative and semi-radiative blast waves, and can describe the effects of
a time-varying radiative efficiency. The equations we present are valid for
arbitrary density profiles, and also for a circum-burst medium enriched with
electron-positron pairs. The presence of pairs enhances the fraction of shock
energy gained by the leptons, thus increasing the importance of radiative
losses. Our model allows to study whether the high-energy (>0.1 GeV) emission
in GRBs may originate from afterglow radiation. In particular, it is suitable
to test whether the fast decay of the high-energy light curve observed in
several Fermi LAT GRBs can be ascribed to an initial radiative phase, followed
by the standard adiabatic evolution.
