Justification of the quasi-averaged equations of one-dimensional motion of a viscous barotropic medium with rapidly oscillating properties (Q1360742)

In [Dokl. Akad. Nauk SSSR 268, 836-840 (1983); translation in Sov. Phys., Dokl. 28, 125-127 (1983; Zbl 0569.35067)], \textit{N. S. Bakhvalov} and \textit{M. E. Ehglit} proposed a new approach to describe the problems of the one-dimensional dynamics of a viscous compressible medium with rapidly oscillating properties. This approach leads to systems of equations that contain both slow and fast variables, which are called quasi-averaged. In this work, a similar justification is given for the case of a barotropic medium. Namely, the existence and uniqueness ``in the large'' (with respect to time and data) of the generalized solutions to the basic inhomogeneous initial-boundary problems for a system of quasi-averaged equations are obtained. We establish a limit connection between solutions to the initial-boundary problems for a system of equations of the one-dimensional motion of a viscous medium with nonsmooth rapidly oscillating data and solutions to the system of Bakhvalov-Eglit quasi-averaged equations.