On a singularly perturbed,coupled parabolic–parabolic problem

Abstract

In this paper we study a model for convection–diffusion processes in which (1) the characters of both diffusion and convection change discontinuously at an internal domain point, (2) there is a small parameter ε, making it a singular perturbation problem, and (3) one of the boundary conditions is nonlinear. Specifically, the problem is (S_ε), (BC_ε), (IC_ε), (TC_ε) formulated below. The problem is singularly perturbed with respect to the uniform convergence topology, with an internal transition layer. An asymptotic expansion of order zero for the solution is determined formally. Then some estimates for the remainder components are established to validate our expansion.