  We present an ordinary case in the momentum diffusion equation for the
electron spectrum evolution and investigate the energy spectra and time
dependent properties of flare in Mrk 421 in the frame of a time-dependent
one-zone synchrotron self-Compton model. In this model, electrons are
accelerated to extra-relativistic energy through the strong magnetic turbulence
and evolve with time, and non-thermal photons are produced by both synchrotron
and inverse Comtpon scattering off synchrotron photons. Moreover, non-thermal
photons during a pre-flare are produced by the relativistic electrons in the
steady state and those during a flare are produced by the electrons whose
injection rate is changed during some time interval. We apply the model to the
energy spectra and time-dependent properties of flares in Mrk 421 by
reproducing the pre-burst spectrum of the source and varying the injection rate
in the Bohm diffusion (q=1) and the hard sphere approximation (q=2) case,
respectively. Our results show that Bohm diffusion case leads to hard photon
spectra, and hard sphere case approximation seems to reproduce the energy
spectra and the time dependent properties of flare still better.
