  In this paper, the one-dimensional compressible Navier-Stokes system with
outer pressure boundary conditions is investigated. Under some suitable
assumptions, we prove that the specific volume and the temperature are bounded
from below and above independently of time, and then give the local and global
existence of strong solutions. Furthermore, we also obtain the convergence of
the global strong solution to a stationary state and the nonlinearly stability
of its convergence. It is worth noticing that all the assumptions imposed on
the initial data are the same as Takeyuki Nagasawa [Japan.J.Appl.Math.(1988)].
Therefore, our work can be regarded as an improvement of the results of
Takeyuki.
