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Asymptotic behaviour of a singularly perturbed convection-diffusion problem in a rectangle with discontinuous Dirichlet data

Opened Access Asymptotic behaviour of a singularly perturbed convection-diffusion problem in a rectangle with discontinuous Dirichlet data
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Autor: López García, José Luis
Pérez Sinusía, Ester
Fecha: 2007-09
Publicado en: XX Congreso de Ecuaciones Diferenciales y Aplicaciones. Sevilla, 24-28 de septiembre de 2007
Tipo de documento: Ponencia
Resumen: We consider a singularly perturbed convection-diffusion equation, −ε△u+ −→v · −→∇u = 0, defined on a rectangular domain Ω ≡ {(x, y)| 0 ≤ x ≤ πa, 0 ≤ y ≤ π}, a > 0, with Dirichlet-type boundary conditions discontinuous at the points (0, 0) and (πa, 0): u(x, 0) = 1, u(x, π) = u(0, y) = u(πa, y) = 0. An asymptotic expansion of the solution is obtained from a a series representation in two limits: a) when the singular parameter ε → 0 + (with fixed distance to the points (0, 0) and (πa, 0)) and b) when (x, y) → (0, 0) or (x, y) → (πa, 0) (with fixed ε). It is shown that the first term of the expansion at ε = 0 contains a linear combination of error functions. This term characterizes the effect of the discontinuities on the ε−behaviour of the solution u(x, y) in the boundary or the internal layers. On the other hand, near the points of discontinuity (0, 0) and (πa, 0), the solution u(x, y) is approximated by a linear function of the polar angle.
Tamaño: 299.0Kb
Formato: PDF

URI: http://hdl.handle.net/11441/35802

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