We determine the schedule for the diffusive evolution of isoconcentration ‘‘surfaces’’ into a semi-infinite region, initially empty of diffusant, for a particular time-invariant boundary condition corresponding to constant diffusant concentration. This result is obtained by exploiting the correspondence between solutions of the Fokker-Planck equation for this boundary-value problem and the known fundamental solution in an unbounded space. We find that the initial evolution is linear, as predicted by us in earlier work, while the long-time behavior is as ${\mathit{t}}^{1/2}$, which is the solution predicted from the diffusion equation over the entire time domain. The transition between these limiting regions is described by a more complicated functional dependence.

• Received 10 May 1990

DOI:https://doi.org/10.1103/PhysRevA.42.3504