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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| Format: | Article |
| Language: | English |
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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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| author | Gung-Min Gie Chang-Yeol Jung Roger Temam |
| author_facet | Gung-Min Gie Chang-Yeol Jung Roger Temam |
| author_sort | Gung-Min Gie |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-b61d95a1937047edba2f63f0b8c6256e |
| institution | DOAJ |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-b61d95a1937047edba2f63f0b8c6256e2025-08-20T03:20:55ZengWileyInternational Journal of Differential Equations1687-96431687-96512013-01-01201310.1155/2013/532987532987Analysis of Mixed Elliptic and Parabolic Boundary Layers with CornersGung-Min Gie0Chang-Yeol Jung1Roger Temam2Department of Mathematics, University of California, Riverside, 900 University Avenue, Riverside, CA 92521, USAUlsan National Institute of Science and Technology, San 194, Banyeon-ri, Eonyang-eup, Ulju Gun, Ulsan 689-798, Republic of KoreaThe Institute for Scientific Computing and Applied Mathematics, Indiana University, 831 East Third Street, Bloomington, IN 47405, USAWe 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.http://dx.doi.org/10.1155/2013/532987 |
| spellingShingle | Gung-Min Gie Chang-Yeol Jung Roger Temam Analysis of Mixed Elliptic and Parabolic Boundary Layers with Corners International Journal of Differential Equations |
| title | Analysis of Mixed Elliptic and Parabolic Boundary Layers with Corners |
| title_full | Analysis of Mixed Elliptic and Parabolic Boundary Layers with Corners |
| title_fullStr | Analysis of Mixed Elliptic and Parabolic Boundary Layers with Corners |
| title_full_unstemmed | Analysis of Mixed Elliptic and Parabolic Boundary Layers with Corners |
| title_short | Analysis of Mixed Elliptic and Parabolic Boundary Layers with Corners |
| title_sort | analysis of mixed elliptic and parabolic boundary layers with corners |
| url | http://dx.doi.org/10.1155/2013/532987 |
| work_keys_str_mv | AT gungmingie analysisofmixedellipticandparabolicboundarylayerswithcorners AT changyeoljung analysisofmixedellipticandparabolicboundarylayerswithcorners AT rogertemam analysisofmixedellipticandparabolicboundarylayerswithcorners |