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The paper considers the evolution of the supernova envelopes produced byPopulation III stars with masses of $M_*\sim 25-200 M_\odot$ located innon-rotating protogalaxies with masses of $M\sim 10^7 M_\odot$ at redshifts$z=12$, with dark-matter density profiles in the form of modified isothermalspheres. The supernova explosion occurs in the ionization zone formed by asingle parent star. The properties of the distribution of heavy elements(metals) produced by the parent star are investigated, as well as theefficiency with which they are mixed with the primordial gas in the supernovaenvelope. In supernovae with high energies ($E\simgt 5\times 10^{52}$ erg), anappreciable fraction of the gas can be ejected from the protogalaxy, but nearlyall the heavy elements remain in the protogalaxy. In explosions with lowerenergies ($E\simlt 3\times 10^{52}$ erg), essentially no gas and heavy elementsare lost from the protogalaxy: during the first one to threemillion years, thegas and heavy elements are actively carried from the central region of theprotogalaxy ($r\sim 0.1 r_{vir}$, where $r_{vir}$ is the virial radius of theprotogalaxy), but an appreciable fraction of the mass of metals subsequentlyreturns when the hot cavity cools and the envelope collapses. Supernovae withhigh energies ($E\simgt 5\times 10^{52}$ erg) are characterized by a very lowefficiency of mixing of metals; their heavy elements are located in the smallvolume occupied by the disrupted envelope (in a volume comparable with that ofthe entire envelope), with most of the metals remaining inside the hot,rarified cavity of the envelope. (abridged)

Evolution of the First Supernovae in Protogalaxies: Dynamics of Mixing of Heavy Elements