Strong shock in the uniformly expanding medium
  Propagation of the strong shock in the flat expanding Friedman universe is investigated using methods of dimension and similarity. Exact analytic solution of self-similar equations is obtained, determining dependences of the radius and velocity of the shock wave on time and radius. It is obtained, that in the expanding medium the velocity of shock decreases as $\sim t^{-1/5}$, what is slower than the shock velocity in the static uniform medium $\sim t^{-3/5}$. The radius of the shock wave in the expanding self-gravitating medium increases $\sim t^{4/5}$, more rapidly than the shock wave radius in the uniform non-gravitating medium $\sim t^{2/5}$. So, the shock propagates in the direction of decreasing density with larger speed, that in the static medium, due to accelerating action of the decreasing density, even in the presence of a self-gravitation. 
G.S. Bisnovatyi-Kogan
astro-ph.CO math-ph math.MP