  We simulate the emission in the shallow decay phase of gamma-ray burst
afterglows using a time-dependent code. We test four models: the energy
injection model, evolving the injection efficiency of non-thermal electrons,
evolving the amplification of the magnetic field, and the wind model with a
relatively low bulk Lorentz factor. All of the four models can reproduce the
typical X-ray afterglow lightcurve. The spectral shape depends on not only the
parameter values at the time corresponding to the observer time but also the
past evolution of the parameters. The model differences appear in the evolution
of the broadband spectrum, especially in the inverse Compton component. Future
gamma-ray observations with imaging atmospheric Cherenkov telescopes such as
CTA will reveal the mechanism of the shallow decay phase.
