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Kinetic Equation for Homogenization of a One-Dimensional Model of Dynamics of a Mixture of Viscous Barotropic Gases

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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– Églit equations. The proof is based on construction of two-scale Young measures.

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  1. Lavrentyev Institute of Hydrodynamics of the Siberian Branch of the RAS, 15, Ac. Lavrentieva pr., Novosibirsk, 630090, Russia

    S. A. Sazhenkov

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  1. S. A. Sazhenkov
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Correspondence to S. A. Sazhenkov.

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Translated from Problemy Matematicheskogo Analiza 80, April 2015, pp. 95-106.

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Sazhenkov, S.A. Kinetic Equation for Homogenization of a One-Dimensional Model of Dynamics of a Mixture of Viscous Barotropic Gases. J Math Sci 208, 253–266 (2015). https://doi.org/10.1007/s10958-015-2443-0

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  • DOI: https://doi.org/10.1007/s10958-015-2443-0

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