  We present results of a detailed numerical study and theoretical analysis of
the dynamics of internal shocks in relativistic jets and the non-thermal flares
associated with these shocks. In our model internal shocks result from
collisions of density inhomogeneities (shells) in relativistic jet flows. We
find that the merged shell resulting from the inelastic collision of shells has
a complicated internal structure due to the non-linear dynamics of the
interaction. Furthermore, the instantaneous efficiency for converting kinetic
energy into thermal energy is found to be almost twice as high as theoretically
expected during the period of significant emission. The Lorentz factors of the
internal shocks are correlated with the initial inertial masses of the shells.
  Because of the complexity of the non-linear evolution the merged shell
becomes very inhomogeneous and simple one-zone models are inadequate to extract
physical parameters of the emitting region from the resulting light curves. In
order to improve on these one-zone approximations, we propose a novel way of
analyzing the space-time properties of the emission. Based on these properties
we construct an analytic model of non-thermal flares which can be used to
constrain some (unobservable) physical parameters of the internal shocks. These
are the ratio of the Lorentz factors between the forward and the reverse shock
(caused by the shell collision), and the shell crossing times of these shocks.
The analytic model is validated by applying it to the synthetic light curves
computed from our models. It can equally well be applied to observations.
