Unique solvability of initial-boundary value problem for a model system of equations for the polytropic motion of a mixture of viscous compressible fluids

The initial-boundary value problem is considered for a model system of one-dimensional equations describing unsteady polytropic motion of a mixture of viscous compressible fluids. The existence and uniqueness theorem is proved for a strong solution of the problem without restrictions on the structure of the viscosity matrices, except standard requirements of symmetry and positive definiteness.