Boundary layer theory for convection-diffusion equations in a circle
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- Boundary layer theory for convection-diffusion equations in a circle
- Jung, Chang-Yeol; Temam, Roger M.
- Boundary layers; Characteristic points; Convection-dominated problems; Parabolic boundary layers; Singular perturbations
- Issue Date
- TURPION LTD
- RUSSIAN MATHEMATICAL SURVEYS, v.69, no.3, pp.435 - 480
- 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:  dealt with the case where the function f is sufficiently flat at the characteristic points, the so-called compatible case;  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.
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