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We study transport processes of interacting Bose-Einstein condensates in presence of dimensionally restricted disorder potentials. Our numerical approach is based on the integration of the Gross-Pitaevskii equation in presence of an external source that simulates the quasi-stationary injection of coherent matter waves onto the disorder potential. For the case of one-dimensional disorder potentials, we find that the presence of the atom-atom interaction leads to a cross-over from an exponential to an algebraic decrease of the average transmission with the disorder sample length, what represents a significant deviation from the phenomenon of Anderson localization. For two-dimensional disorder potentials, the presence of interaction has an appreciable impact on the scenario of weak localization and modifies specifically the height of the coherent backscattering peak. |