Global solvability of the equations for compressible miscible flows in porous media

The global solvability of the one-dimensional equations that govern compressible miscible flows in porous media is presented. The pressure and density are related by the equation of state, if the mixture is weakly compressible. The mass concentration of each of the components is described by the equation, if the chemical reactions between the fluid components are neglected. The three different parabolic systems to which the original equations of motion are reduced, proved to be equivalent to the original equations. The conditions for the concentrations are satisfied at any time, if a weak solution is sufficiently smooth and the initial data lie in domain. The main purpose of system is that it is used to construct approximate solutions, while their norms satisfy a priori estimates in the function spaces appearing in the definition of a weak solution. The Langrangian system also is used to determine Galerkin approximations for the satisfaction of the equations.