  We numerically explore the long-time expansion of a one-dimensional
Bose-Einstein condensate in a disorder potential employing the Gross-Pitaevskii
equation. The goal is to search for unique signatures of Anderson localization
in the presence of particle-particle interactions. Using typical experimental
parameters we show that the time scale for which the non-equilibrium dynamics
of the interacting system begins to diverge from the non-interacting system
exceeds the observation times up to now accessible in the experiment. We find
evidence that the long-time evolution of the wavepacket is characterized by
(sub)diffusive spreading and a growing effective localization length suggesting
that interactions destroy Anderson localization.
