  Bubbles in the interstellar medium are produced by astrophysical sources,
which continuously or explosively deposit large amount of energy into the
ambient medium. These expanding bubbles can drive shocks in front of them,
which dynamics is markedly different from the widely used Sedov-von
Neumann-Taylor blast wave solution. Here we present the theory of a
bubble-driven shock and show how its properties and evolution are determined by
the temporal history of the source energy output, generally referred to as the
source luminosity law, $L(t)$. In particular, we find the analytical solutions
for a driven shock in two cases: the self-similar scaling $L\propto (t/t_s)^p$
law (with $p$ and $t_s$ being constants) and the finite activity time case,
$L\propto (1-t/t_s)^{-p}$. The latter with $p>0$ describes a
finite-time-singular behavior, which is relevant to a wide variety of systems
with explosive-type energy release. For both luminosity laws, we derived the
conditions needed for the driven shock to exist and predict the shock
observational signatures. Our results can be relevant to stellar systems with
strong winds, merging neutron star/magnetar/black hole systems, and massive
stars evolving to supernovae explosions.
