  We consider the compressible Navier-Stokes equations for isentropic dynamics
with real viscosity on a bounded interval. In the case of boundary data
defining an admissible shock wave for the corresponding unviscous hyperbolic
system, we determine a scalar differential equation describing the motion of
the internal transition layer. In particular, for small viscosity, the velocity
of the motion is exponentially small. The approach is based on the construction
of a one-parameter manifold of approximate solutions and on an appropriate
projection of the evolution of the complete Navier-Stokes system towards such
manifold.
