Convection-dominated problems in a circle domain

In this article we aim to study the boundary layer generated by a convection-diffusion equation in a circle. In the model problem that we consider two characteristic points appear. To the best of our knowledge such boundary layer problems have not been studied in a systematic way yet and we indeed know that very complex situations can occur. In the cases that we consider in the present article certain simplifying compatibility conditions are assumed. Other situations will be addressed which involve noncompatible data, or more general domains