  We present the generalization of the Sedov-Taylor self-similar strong
spherical shock solution for the case of a central energy source varying in
time, $E=A t^k$, where $A$ and $k$ are constants. The known Sedov-Taylor
solution corresponds to a particular adiabatic case of $k=0$ or \emph{instant
shock} with an instant energy source of the shock, $E=A$. The self-similar
hydrodynamic flow in the nonadiabatic $k\neq0$ case exists only under the
appropriate local entropy (energy) input which must be supported by some
radiative mechanism from the central engine. The specific case of $k=1$
corresponds to a permanent energy injection into the shock, or injection shock
with a central source of constant luminosity, $L=A$, $E=A t$. The generalized
self-similar shock solution may be applied to astrophysical objects in which
the duration of central source activity is longer than the shock expansion
time, e.g. the early phase of SN explosions, strong wind from stars and young
pulsars, non-steady spherical outflow from black holes and collapsing dense
stellar clusters with numerous neutron star collisions.
