A note on the axisymmetric diffusion equation

Abstract

We consider the explicit solution to the axisymmetric diffusion equation. We recast the solution in the form of a Mellin inversion formula, and outline a method to compute a formula for \(u(r,t)\) as a series using the Cauchy residue theorem. As a consequence, we are able to represent the solution to the axisymmetric diffusion equation as a rapidly converging series.

doi:10.1017/S1446181121000110