  Motivated by practical applications in heat conduction and contaminant
transport, we consider heat and mass diffusion across a perturbed interface
separating two finite regions of distinct diffusivity. Under the assumption of
continuity of the solution and diffusive flux at the interface, we use
perturbation theory to develop an asymptotic expansion of the solution valid
for small perturbations. Each term in the asymptotic expansion satisfies an
initial-boundary value problem on the unperturbed domain subject to interface
conditions depending on the previously determined terms in the asymptotic
expansion. Demonstration of the perturbation solution is carried out for a
specific, practically-relevant set of initial and boundary conditions with
semi-analytical solutions of the initial-boundary value problems developed
using standard Laplace transform and eigenfunction expansion techniques.
Results for several choices of the perturbed interface confirm the perturbation
solution is in good agreement with a standard numerical solution.
