Abstract
We consider the one-dimensional model of the dynamics of a mixture of viscous barotropic gases with rapidly oscillating initial distribution of the specific volume. We rigorously justify the homogenization procedure as the frequency of rapid oscillations tends to infinity. We construct a closed limit effective model of the mixture motion containing an additional kinetic equation that carries a complete information on the evolution of the limit oscillations modes. It is shown that for periodic initial data the constructed limit model is reduced to a system of quasihomogenized Bakhvalov– Eglit equations. The proof is based on construction of two-scale Young measures.
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