, Volume 48, Issue 8, pp 1137-1152

Version of the homogenized Bakhvalov-Eglit model with kinetic equation for the evolution of oscillations

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Abstract

We consider the one-dimensional model of the dynamics of a viscous barotropic gas with rapidly oscillating initial distributions 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 gas motion containing an additional kinetic equation that carries complete information on the evolution of the limit oscillation modes. We show that if the initial data are periodic, then the constructed limit model can be reduced to a system of quasi-homogenized Bakhvalov-Eglit equations.

Original Russian Text © S.A. Sazhenkov, 2012, published in Differentsial’nye Uravneniya, 2012, Vol. 48, No. 8, pp. 1150–1165.