Асимптотическое поведение решения начально-краевой задачи одномерного движения вязкой баротропной многокомпонентной смеси

The asymptotic behavior (as $t\rightarrow +\infty$) of the solution to the initial-boundary value problem is analyzed for the system of differential equations describing the barotropic dynamics of a viscous  multifluid with a non-diagonal, symmetric and positive definite viscosity matrix, in the case of one spatial variable. New a priori estimates are obtained and stabilization of the solution to the initial-boundary value problem is proved.