  We treat the 1D shock tube problem, establishing existence of steady
solutions of full (nonisentropic) polytropic gas dynamics with arbitrary
noncharacteristic data. We present also numerical experiments indicating
uniqueness and time-asymptotic stability of such solutions. At the same time,
we give an example of an (artificial) equation of state possessing a convex
entropy for which there holds nonuniqueness of solutions. This is associated
with instability and Hopf bifurcation to time-periodic solutions. In a second
part, we study general systems of viscous conservation laws and we state
results on existence, stability and spectral stability of steady states in
restricted cases.
