  We model the expansion of an interacting atomic Bose-Einstein condensate in a
disordered lattice with a nonlinear diffusion equation normally used for a
variety of classical systems. We find approximate solutions of the diffusion
equation that well reproduce the experimental observations for both short and
asymptotic expansion times. Our study establishes a connection between the
peculiar shape of the expanding density profiles and the microscopic nonlinear
diffusion coefficients.
