The Separability of the Diffusion Equation with Drift Term
A. Seeger · physica status solidi (b) · 1970
Abstract The paper investigates the diffusion equation with drift term, ∂C/∂t = div (D grad C + + μ C grad U), in particular the question of its separability in three dimensions. (D is the diffusion coefficient, μ the mobility, both assumed to be constant scalar quantities; U denotes the potential giving rise to the drift.) The transformation to a new dependent variable f = C exp (μ U/2 D) transforms the equation into a Schrödinger equation. Using this it is shown that, for appropriate choices of the potentials U, the diffusion‐drift equation is separable with modulation factor in the ellipsoidal coordinates (and its degenerate special cases) but in no other coordinate systems. The conditions to which U has to be subjected in order to lead to separability are stated and shown to have a close relationship to the factorization of the solutions of the original equation.