Something has been bothering me recently regarding a diffusion problem. Consider a source of particles in a box, diffusing outwards. Set the boundary conditions so that the density is zero at the edge of the box. We can solve this problem in "steady state" and we find essentially a parabolic (or x^2) dependence of the density inside the box, dropping away from the source. However, since the density is zero at the boundaries of the box, the mass flux there is zero (rho*v*A). What's going on here? How can we have a steady state problem with mass clearly leaving the box without any mass flow actually going out of the box? Does this simply mean that the mass interpretation is incorrect for this example?