Analysis of Mixed Elliptic and Parabolic Boundary Layers with Corners
We study the asymptotic behavior at small diffusivity of the solutions, uε, to a convection-diffusion equation in a rectangular domain Ω. The diffusive equation is supplemented with a Dirichlet boundary condition, which is smooth along the edges and continuous at the corners. To resolve the discrepa...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2013/532987 |
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| Summary: | We study the asymptotic behavior at small diffusivity of the solutions,
uε, to a convection-diffusion equation in a rectangular domain Ω. 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 ∂Ω, 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 Ω, 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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| ISSN: | 1687-9643 1687-9651 |