  Recent observations of Gamma-Ray Bursts (GRBs) by the Fermi Large Area
Telescope (LAT) revealed a power law decay feature of the high energy emission
(above 100 MeV), which led to the suggestion that it originates from a
(probably radiative) external shock. We analyze four GRBs (080916C, 090510,
090902B and 090926A) jointly detected by Fermi LAT and Gamma-ray Burst Monitor
(GBM), which have high quality lightcurves in both instrument energy bands.
Using the MeV prompt emission (GBM) data, we can record the energy output from
the central engine as a function of time. Assuming a constant radiative
efficiency, we are able to track energy accumulation in the external shock
using our internal/external shell model code. By solving for the early
evolution of both an adiabatic and a radiative blastwave, we calculate the high
energy emission lightcurve in the LAT band and compare it with the observed one
for each burst. The late time LAT light curves after T90 can be well fit by the
model. However, due to continuous energy injection into the blastwave during
the prompt emission phase, the early external shock emission cannot account for
the observed GeV flux level. The high energy emission during the prompt phase
(before T90) is most likely a superposition of a gradually enhancing external
shock component and a dominant emission component that is of an internal
origin.
