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

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Analysis of mixed elliptic and parabolic boundary layers with corners

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Title
Analysis of mixed elliptic and parabolic boundary layers with corners
Author
Jung, Chang-YeolGie, Gung-MinTemam, Roger
Issue Date
201304
Publisher
HINDAWI PUBLISHING CORP
Citation
INTERNATIONAL JOURNAL OF DIFFERENTIAL EQUATIONS, v.2013, no., pp.532987 -
Abstract
We study the asymptotic behavior at small diffusivity of the solutions, uε, to a convection-diffusion equation in a rectangular domain. The diffusive equation is supplemented with a Dirichlet boundary condition, which is smooth along the edges and continuous at the corners. To resolve the discrepancy, on ∂, between uε and the corresponding limit solution, u0, we propose asymptotic expansions of uε at any arbitrary, but fixed, order. In order to manage some singular effects near the four corners of , the so-called elliptic and ordinary corner correctors are added in the asymptotic expansions as well as the parabolic and classical boundary layer functions. Then, performing the energy estimates on the difference of uε and the proposed expansions, the validity of our asymptotic expansions is established in suitable Sobolev spaces.
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DOI
http://dx.doi.org/10.1155/2013/532987
ISSN
1687-9643
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SNS_Journal Papers
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