Strong Shock in the Uniformly Expanding Universe with a Spherical Void

Propagation of strong shock wave in the expanding universe is studied using approximate analytic, and exact numerical solution of self-similar equations. Both solutions have similar properties, which change qualitatively, depending on the adiabatic powers $\gamma$. In the interval $1<\gamma<\gamma_{cr} \sim 1.16$ analytic and numeric solutions fill all the space without any voids and they are rather close to each other. At larger $\gamma>\gamma_{cr}$ a pressure becomes zero at finite radius, and a spherical void appears around the origin in both solutions. All matter is collected in thin layer behind the shock wave front. The structure of this layer qualitatively depends on $\gamma$. At the inner edge of the layer the pressure is always zero, but the density on this edge is jumping from zero to infinity at $\gamma \approx 1.4$ in both solutions.