Strong Shock in a Uniform Expanding Universe. Approximate and Exact Solutions of Self-Similar Equations

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Self-similar solution is obtained for propagation of a strong shock, in a flat expanding dusty Friedman universe. Approximate analytic solution was obtained earlier, using relation between self-similar variables, equivalent to the exact energy conservation integral, which was obtained by L.I. Sedov for the strong explosion in the static uniform medium. Here, numerical integration of self-similar equation is performed, providing an exact solution of the problem, which is rather close to the approximate analytic one. The differences between these solutions are most apparent in the vicinity of the shock. For a polytropic equation of state, self-similar solutions exist in a more narrow interval of the adiabatic power than in the static case.