The problem of a spherical shock front generated in a point explosion and traveling in a homogeneous medium is analytically studied with account for counterpressure on the entire infinite interval of its existence. For this purpose, asymptotic representations of the excess pressure in the shock wave near and far away from the energy release point are matched. It is possible analytically to continue the four-term expansion for the far zone involving unknown constants, so that it rigorously coincides with the four-term power expansion of the solution for the singular point, that is, the blast center. The problem of determination of the unknown constants is mathematically closed by the derived entropy loss integral which expresses the global energy conservation law. The analytical dependence of the excess pressure in the shock wave on distance thus obtained is in good agreement with the results of numerical calculations.
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