Geodesic
Boundary layer theory for convection-diffusion equations in a~circle
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 69 (2014) no. 3, pp. 435-480

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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.
Keywords: boundary layers, characteristic points, convection-dominated problems, parabolic boundary layers.
Mots-clés : singular perturbations 
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     title = {Boundary layer theory for convection-diffusion equations in a~circle},
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Ch.-Y. Jung; R. Temam. Boundary layer theory for convection-diffusion equations in a~circle. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 69 (2014) no. 3, pp. 435-480. http://geodesic.mathdoc.fr/item/RM_2014_69_3_a2/