Local solvability of an approximate problem for one-dimensional equations of dynamics of viscous compressible heat-conducting multifluids

The problem of one-dimensional unsteady motion of a heat-conducting viscous compressible multifluid (mixture of perfect gases) on a bounded interval is considered, and the viscosity matrix is not assumed to be diagonal. The first step is made in proving the solvability of this problem: the local solvability of the approximate problem (for the Galerkin approximations) is shown.