X-ray and γ-ray variability of Mrk 421

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 Compton 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 the Bohm diffusion case leads to hard photon spectra, and the hard sphere case approximation seems to reproduce the energy spectra and the time-dependent properties of flare still better.