An unsteady problem of the point explosion theory in Lagrangian coordinates is considered. The process of reorganization of gas flow in the area covered by a blast-wave is investigated. In a numerical experiment with variation of non-dimensional governing parameters of the problem, the features of such a flow have been identified for the first time. It was found that, except for the nodal point singularity in the center of energy release, determined by the initial conditions of the problem (L.I. Sedov's self- similar solution), extra singular focus, saddle and node points are formed in the disturbed flow area with time.
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