Boundary layer theory for convection-diffusion equations in a circle

This paper is devoted to boundary layer theory for singularly perturbed convection-diffusion equations in the unit circle. Two characteristic points appear, $(\pm 1,0)$, in the context of the equations considered here, and singularities may occur at these points depending on the behaviour there of a given function $f$, namely, the flatness or compatibility of $f$ at these points as explained below. Two previous articles addressed two particular cases: [24] dealt with the case where the function $f$ is sufficiently flat at the characteristic points, the so-called compatible case; [25] dealt with a generic non-compatible case ($f$ polynomial). This survey article recalls the essential results from those papers, and continues with the general case ($f$ non-flat and non-polynomial) for which new specific boundary layer functions of parabolic type are introduced in addition.
Bibliography: 49 titles.