On bounds for solutions to finite-difference equations for one- dimensional flow of viscous barotropic gas (Q1842497)

Some new a priori estimates are presented for the title problem in terms of the state equation \(p = p(\eta)\), where \(p\) is pressure and \(\eta\) is specific volume. In particular, a general estimate is given which does not depend on the behaviour of \({dp \over d \eta}\), and an important case is considered where the function \(p(\eta)\) is defined not on the whole semi-axis \(\mathbb{R}^ +\), but only for \(\eta > b > 0\) being not monotone nor bounded. The results obtained are used to derive the uniqueness conditions for two-layer difference schemes approximating the equations of magnetic barotropic gas dynamics.