A singular perturbation problem with discontinuous data in a cuboid

Abstract

We analyse the asymptotic behaviour of the solution of a 3D singularly perturbed convection-diffusion problem with discontinuous Dirichlet boundary data defined in a cuboid. We write the solution in terms of a double series and we obtain an asymptotic approximation of the solution when the singular parameter e → 0. This approximation is given in terms of a finite combination of products of error functions and characterizes the effect of the discontinuities on the small e-behaviour of the solution in the singular layers.