Summary: The Navier-Stokes equations of a compressible barotropic
fluid in 1D with zero velocity boundary conditions are considered. We study
the case of large initial data in $H^1$ as well as the mass force such
that the stationary density is positive. The uniform lower bound for the
density is proved. By constructing suitable Lyapunov functionals, decay
rate estimates in $L^2-$norm and $H^1-$norm are given. The decay rate is
exponential if so the decay rate of nonstationary part of the mass force
is. The results are proved in the Eulerian coordinates for a wide class
of increasing state functions including $p(\rho )=p_1\rho^\gamma$ with
any $\gamma >0.$ We also extend the results for equations of multicomponent
compressible barotropic mixture (in the absence of chemical reactions).
MSC (2000) Subject Classification: 35Q30, 35B40, 76N15
Keywords: Compressible fluid, Navier-Stokes equations, asymptotic
behavior