  We study the inflow-outflow boundary value problem on an interval, the analog
of the 1D shock tube problem for gas dynamics, for general systems of
hyperbolic-parabolic conservation laws. In a first set of investigations, we
study existence, uniqueness, and stability, showing in particular local
existence, uniqueness, and stability of small amplitude solutions for general
symmetrizable systems. In a second set of investigations, we investigate
structure and behavior in the small- and large-viscosity limits. A phenomenon
of particular interest is the generic appearance of characteristic boundary
layers in the inviscid limit, arising from noncharacteristic data for the
viscous problem, even of arbitrarily small amplitude. This induces an
interesting new type of \transcharacteristic" hyperbolic boundary condition
governing the formal inviscid limit.
