Rapid variability in the synchrotron self Compton model for blazars
  Blazars are characterized by large amplitude and fast variability, indicating that the electron distribution is rapidly changing, often on time scales shorter than the light crossing time. The emitting region is sufficiently compact to let radiative losses dominate the cooling of high energy electrons. We study the time dependent behaviour of the electron distribution after episodic electron injection phases, and calculate the observed synchrotron and self Compton radiation spectra. Since photons produced in different part of the source have different travel times, the observed spectrum is produced by the electron distribution at different stages of evolution. Even a homogeneous source then resembles an inhomogeneous one. Time delays between the light curves of fluxes at different frequencies are possible, as illustrated for the specific case of the BL Lac object Mkn 421. 
Marco Chiaberge and Gabriele Ghisellini