Solution of multilayer diffusion problems via the Laplace transform

We consider a one-dimensional multilayer diffusion problem subject to nonhomogeneous boundary conditions. Unlike previous results that used a separation of variables technique to solve such problems with homogeneous boundary conditions, here we use a Laplace transform approach. We reformulate the multilayer diffusion problem as a sequence of one-layer diffusion problems with arbitrary time-dependent functions, solve a general one-layer diffusion problem using the Laplace transform, and then use the interface conditions to determine a system of renewal-type equations for the time-dependent functions. Finally, these renewal equations are solved explicitly using the Laplace transform.