Diffusion in a composite slab consisting of a large number of layers provides an ideal
prototype problem for developing and analysing two-scale modelling approaches for …

We develop a new semi-analytical method for solving multilayer diffusion problems with time-
varying external boundary conditions and general internal boundary conditions at the …

This article presents a theoretical analysis of a one-dimensional heat transfer problem in two
layers involving diffusion, advection, internal heat generation or loss linearly dependent on …

We study the lattice random walk dynamics in a heterogeneous space of two media
separated by an interface and having different diffusivity and bias. Depending on the …

The interface problem for the linear Korteweg–de Vries (KdV) equation in one-dimensional
piecewise homogeneous domains is examined by constructing an explicit solution in each …

We present an efficient method to compute the eigenvalues and eigenmodes of the diffusion
operator ∇ (D ∇)∇(D∇) on one-dimensional heterogeneous structures with multiple semi …

We demonstrate the use of the Unified Transform Method or Method of Fokas for boundary
value problems for systems of constant-coefficient linear partial differential equations. We …

The problem of heat conduction on networks of multiply connected rods is solved by
providing an explicit solution of the one-dimensional heat equation in each domain. The size …

The problem of mass diffusion in layered systems has relevance to applications in different
scientific disciplines, eg, chemistry, material science, soil science, and biomedical …

The problem of heat conduction in one-dimensional piecewise homogeneous composite
materials is examined by providing an explicit solution of the one-dimensional heat equation …