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Uspekhi Mat. Nauk, 2014, Volume 69, Issue 3(417), Pages 43–86 (Mi umn9584)  

This article is cited in 6 scientific papers (total in 6 papers)

Boundary layer theory for convection-diffusion equations in a circle

Ch.-Y. Junga, R. Temamb

a School of Natural Science, Ulsan National Institute of Science and Technology, Ulsan, Republic of Korea
b The Institute for Scientific Computing and Applied Mathematics, Indiana University, Bloomington, U.S.A.

Abstract: 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, singular perturbations, characteristic points, convection-dominated problems, parabolic boundary layers.

Funding Agency Grant Number
National Science Foundation DMS 1206438
Research Fund of Indiana University
National Research Foundation of Korea NRF-2012R1A1B3001167
This work was supported by NSF grant DMS 1206438, by the Research Fund of Indiana University, and by the grant NRF-2012R1A1B3001167 of the National Research Foundation of Korea (NRF), funded by the Government of Korea.


DOI: https://doi.org/10.4213/rm9584

Full text: PDF file (869 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2014, 69:3, 435–480

Bibliographic databases:

Document Type: Article
UDC: 517.95
MSC: 35B25, 35C20, 76D05, 76D10
Received: 25.10.2013

Citation: Ch.-Y. Jung, R. Temam, “Boundary layer theory for convection-diffusion equations in a circle”, Uspekhi Mat. Nauk, 69:3(417) (2014), 43–86; Russian Math. Surveys, 69:3 (2014), 435–480

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Y. Hong, Ch.-Y. Jung, R. Temam, “Singular perturbation analysis of time dependent convection-diffusion equations in a circle”, Nonlinear Anal., 119 (2015), 127–148  crossref  mathscinet  zmath  isi  scopus
    2. G.-M. Gie, Ch.-Y. Jung, R. Temam, “Recent progresses in boundary layer theory”, Discrete Contin. Dyn. Syst., 36:5 (2016), 2521–2583  crossref  mathscinet  zmath  isi  scopus
    3. M. Hamouda, Ch.-Y. Jung, R. Temam, “Boundary layers for the 3D primitive equations in a cube: the supercritical modes”, Nonlinear Anal., 132 (2016), 288–317  crossref  mathscinet  zmath  isi  scopus
    4. A. F. Hegarty, E. O' Riordan, “Numerical solution of a singularly perturbed problem on a circular domain”, Model. i analiz inform. sistem, 23:3 (2016), 349–356  mathnet  crossref  mathscinet  elib
    5. A. F. Hegarty, E. O'Riordan, “Parameter-uniform numerical method for singularly perturbed convection-diffusion problem on a circular domain”, Adv. Comput. Math., 43:5 (2017), 885–909  crossref  mathscinet  zmath  isi  scopus
    6. Hong Y., Jung Ch.-Y., Temam R., “Boundary Layer Analysis For the Stochastic Nonlinear Reaction-Diffusion Equations”, Physica D, 376:SI (2018), 247–258  crossref  mathscinet  isi  scopus
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