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Jung, Chang-Yeol
Analysis and computational methods Lab
Research Interests
  • Analysis, singular perturbations, uncertainty, numerical methods

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Boundary layer theory for convection-diffusion equations in a circle

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Title
Boundary layer theory for convection-diffusion equations in a circle
Author
Jung, Chang-YeolTemam, Roger M.
Keywords
Boundary layers; Characteristic points; Convection-dominated problems; Parabolic boundary layers; Singular perturbations
Issue Date
201406
Publisher
TURPION LTD
Citation
RUSSIAN MATHEMATICAL SURVEYS, v.69, no.3, pp.435 - 480
Abstract
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.
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DOI
http://dx.doi.org/10.1070/RM2014v069n03ABEH004898
ISSN
0036-0279
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