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, (??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.close0