  In this paper a spatially resolved, fully self-consistent SSC model is
presented. The observable spectral energy distribution (SED) evolves entirely
from a low energetic delta distribution of injected electrons by means of the
implemented microphysics of the jet. These are in particular the properties of
the shock and the ambient plasma, which can be varied along the jet axis. Hence
a large variety of scenarios can be computed, e.g. the acceleration of
particles via multiple shocks. Two acceleration processes, shock acceleration
and stochastic acceleration, are taken into account. From the resulting
electron distribution the SED is calculated taking into account synchrotron
radiation, inverse Compton scattering (full cross section) and synchrotron self
absorption. The model can explain SEDs where cooling processes are crucial. It
can verify high variability results from acausal simulations and produce
variability not only via injection of particles, but due to the presence of
multiple shocks. Furthermore a fit of the data, obtained in the 2010
multi-frequency campaign of Mrk501, is presented.
