  A sufficiently powerful astrophysical source with power law luminosity in
time will give rise to a self-similar relativistic blast wave with a reverse
shock traveling into the ejecta and a forward shock moving into the surrounding
medium. Once energy injection ceases and the last energy is delivered to the
shock front, the blast wave will transit into another self-similar stage
depending only on the total amount of energy injected.
  I describe the effect of limited duration energy injection into environments
with density depending on radius as a power law, emphasizing optical / X-ray
Gamma-ray Burst afterglows as applications. The blast wave during injection is
treated analytically, the transition following last energy injection with
one-dimensional simulations. Flux equations for synchrotron emission from the
forward and reverse shock regions are provided. The reverse shock emission can
easily dominate, especially with different magnetizations for both regions.
Reverse shock emission is shown to support both the reported X-ray and optical
correlations between afterglow plateau duration and end time flux,
independently of the luminosity power law slope. The model is demonstrated by
application to bursts 120521A and 090515, and can accommodate their steep
post-plateau light curve slopes.
