  This paper is concerned with nonlinear stability of viscous contact
discontinuity to inflow problem for the one-dimensional full compressible
Navier-Stokes equations with different ends in half space $[0,\infty)$. For the
case when the local stability of the contact discontinuities was first studied
by \cite{X},later generalized by \cite{LX}, local stability of weak viscous
contact discontinuity is well-established by \cite{HMS,HMX,HXY,HZ,HLM2009}, but
for the global stability of inflow gas with big oscillation ends
$(|\theta_+-\theta_-|>1\ and \ |\rho_+-\rho_-|>1)$, fewer results have been
obtained excluding zero dissipation \cite{MaSX} or $\gamma\to 1$ gas see
\cite{HH}. Our main purpose is to deduce the corresponding nonlinear stability
result with the two different ends 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 $|\theta_--\theta_+|>1$ and
$|\rho_--\rho_+|>1$ ,the global stability result holds.
