Boundary layer theory for convection-diffusion equations in a circle

Abstract

This article is related to the boundary layer theory for singularly perturbed convection-di↵usion equations in the unit circle. Two characteristic points appear, (±1, 0), in the context of the equations considered here and singular behaviors may occur at these points depending on the behavior of the given function f at these points, namely, the flatness or compatibility of f at these points as explained below. Two previous articles addressed two particular cases: one dealt with the case where the function f is sufficiently flat at the characteristic points, the socalled compatible case; the other one dealt with a generic noncompatible case (f polynomial). This paper continues with the general case (f non-flat and non-polynomial) for which we additionally introduce new specific boundary layer functions of parabolic type.