  We present a fully analytical, time-dependent leptonic one-zone model that
describes a simplified radiation process of multiple interacting
ultrarelativistic electron populations, accounting for the flaring of GeV
blazars. In this model, several mono-energetic, ultrarelativistic electron
populations are successively and instantaneously injected into the emission
region, i.e., a magnetized plasmoid propagating along the blazar jet, and
subjected to linear, time-independent synchrotron radiative losses, which are
caused by a constant magnetic field, and nonlinear, time-dependent synchrotron
self-Compton radiative losses in the Thomson limit. Considering a general
multiple-injection scenario is, from a physical point of view, more realistic
than the usual single-injection scenario invoked in common blazar models, as
blazar jets may extend over tens of kiloparsecs and, thus, most likely pick up
several particle populations from intermediate clouds. We analytically compute
the electron number density by solving a kinetic equation using Laplace
transformations and the method of matched asymptotic expansions. Moreover, we
explicitly calculate the optically thin synchrotron intensity, the synchrotron
self-Compton intensity in the Thomson limit, as well as the associated total
fluences. In order to mimic injections of finite duration times and radiative
transport, we model flares by sequences of these instantaneous injections,
suitably distributed over the entire emission region. Finally, we present a
parameter study for the total synchrotron and synchrotron self-Compton fluence
spectral energy distributions for a generic three-injection scenario, varying
the magnetic field strength, the Doppler factor, and the initial electron
energy of the first injection in realistic parameter domains, demonstrating
that our model can reproduce the typical broad-band behavior seen in
observational data.
