  This paper is concerned with nonlinear stability of viscous contact
discontinuity to a free boundary problem for the one-dimensional full
compressible Navier-Stokes equations in half space $[0,\infty)$. For the case
when the local stability of the contact discontinuities was first studied by
[1],later generalized by [2], local stability of weak viscous contact
discontinuity is well-established by [4-8], but for the global stability of the
impermeable gas with big oscillation ends $(|\theta_+-\theta_-|>1) $, fewer
results have been obtained excluding zero dissipation [9] or $\gamma\to 1$ gas
see [10]. Our main purpose is to deduce the corresponding nonlinear stability
result with the two different ends to temperature by exploiting the elementary
energy method. As a first step towards this goal, we will show in this paper
that with a certain class of big perturbation which can allow
$|\theta_--\theta_+|>1$, the global stability result holds.
