GRB afterglows: from ultra-relativistic to non-relativistic phase

Postburst evolution of adiabatic fireballs that produce $\gamma$-ray bursts is studied. Emphasis has been put on the transition from the highly relativistic phase to the non-relativistic phase, which, according to our calculation, should happen much earlier than previously expected. The theoretical light curves decline a little sharper at the non-relativistic stage than at early times, but still can fit the observations well. However, disagreements are obvious when $t \ge 100$ d, implying a large initial energy $E_0$, a low interstellar density $n$, or the possible existence of a persistent energy source at the center of the fireball.