  The non-thermal spectra of jetted active galactic nuclei show a variety of
shapes in their low- and high energy components. In some of the brightest
Fermi-LAT blazars, prominent spectral breaks at a few GeV have been regularly
detected, which is inconsistent with conventional cooling effects. We study the
effects of continuous time-dependent injection of electrons into the jet with
differing rates, durations, locations, and power-law spectral indices, and
evaluate its impact on the ambient emitting particle spectrum at a given
snapshot time in the framework of a leptonic blazar emission model. The
emitting electron spectrum is calculated by Compton cooling the continuously
injected electrons, where target photons are assumed to be provided by the
accretion disk and broad line region. We calculate the non-thermal photon
spectra produced by inverse Compton scattering of these external target
radiation fields using the full Compton cross-section in the head-on
approximation. By means of a comprehensive parameter study we present the
resulting ambient electron and photon spectra, and discuss the influence of
each injection parameter. Varying the injection parameters has a notable
influence on the spectral shapes, which can be used to set constraints on the
injection scenarios. We apply our model to the flare state spectral energy
distribution of 3C454.3, and to the FSRQ PKS1510-089. For both sources we show
two different model fits, corresponding to different injection scenarios. In
all four injection scenarios impulsive particle injection is disfavored. Our
model aims towards bridging jet emission with acceleration models using a
phenomenological approach. Blazar spectral data can be analyzed with this model
to constrain injection parameters, in addition to the conventional parameter
values of steady-state emission models, if sufficient broad multifrequency
coverage is provided.
