  We consider the local well-posedness of the one-dimensional nonisentropic
Euler equations with moving physical vacuum boundary condition. The physical
vacuum singularity requires the sound speed to be scaled as the square root of
the distance to the vacuum boundary. The main difficulty lies in the fact that
the system of hyperbolic conservation laws becomes characteristic and
degenerate at the vacuum boundary. Our proof is based on an approximation of
the Euler equations by a degenerate parabolic regularization obtained from a
specific choice of a degenerate artificial viscosity term. Then we construct
the solutions to this degenerate parabolic problem and establish the estimates
that are uniform with respect to the artificial viscosity parameter. Solutions
to the compressible Euler equations are obtained as the limit of the vanishing
artificial viscosity.
  Different from the isentropic case \cite{Coutand4, Lei}, our momentum
equation of conservation laws has an extra term $p_{S}S_x$ that leads to some
extra terms in the energy function and causes more difficulties even for the
case of $\gamma=2$. Moreover, we deal with this free boundary problem starting
from the general cases of $2\leq\gamma<3$ and $1<\gamma<2 $ instead of only
emphasizing the isentropic case of $\gamma=2$ in \cite{Coutand4, jang1, Lei}.
