Partial Differential Equations

Differential Equations

, Volume 48, Issue 8, pp 1137-1152

First online:

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

  • S. A. SazhenkovAffiliated withLavrentyev Institute of Hydrodynamics, Siberian Branch of the Russian Academy of Sciences

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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.