  We study the patterns at which the current flow stabilizes in a 1D
superconducting wire, for various experimentally reasonable boundary
conditions, for small fixed current densities and temperatures close to $T_c$.
We pay special attention to the possible existence of a stationary regime. If
the contacts are superconducting, truly stationary or normal regimes do not
exist, but can be approached as a limit. In the case of weak superconducting
contacts, a rich phase diagram is found, with several periodic regimes that
involve two phase slip centers. For some of these regimes, the density of
Cooper pairs does not have mirror symmetry. If the contacts are normal, the
stationary regime is possible.
