  We theoretically study the influence of weak interactions on the diffusive
expansion of a Bose-Einstein condensate in a three-dimensional random
potential. For this purpose we develop a perturbative approach and calculate
analytically the first-order nonlinear correction to the ensemble-averaged
atomic density as a function of position and time. We find that interactions
renormalize the typical diffusion coefficient of the condensate. The magnitude
of the nonlinear correction is controlled by a single dimensionless parameter
that includes both interaction and disorder strengths.
