Language:   Search:   Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.

Query:
Fill in the form and click »Search«...
Format:
Display: entries per page entries
Zbl 1174.35032
López, José L.; Pérez Sinus\'ia, Ester
(López Garcia, José Luis)
The role of the error function in a singularly perturbed convection-diffusion problem in a rectangle with corner singularities.
(English)
[J] Proc. R. Soc. Edinb., Sect. A, Math. 137, No. 1, 93-109 (2007). ISSN 0308-2105; ISSN 1473-7124/e

The authors deal with an two-dimensional linear elliptic convection-diffusion problems: find a function $u\in C(\overline\Omega)\cap D^2(\Omega)$ such that $$-\varepsilon\Delta u+ v\cdot\nabla u= 0,\quad x\in\Omega\subset \Bbb R^2,$$ $$u|_{\partial\Omega}= f(\widetilde x),\quad \widetilde x\in\partial\Omega,$$ where $\varepsilon$ is a small positive parameter, $V$ is the convection vector, $\widetilde x$ is a variable which lives in $\partial\Omega$, and $D^2(\Omega)$ is the set of functions with partial derivatives up to order two defined in all points of $\Omega$. The authors derive asymptotic expansion of the solution for $\varepsilon\to 0$. Moreover, they derive also asymptotic approximations near the points of discontinuity of the boundary condition.
[Messoud A. Efendiev (Berlin)]
MSC 2000:
*35J25 Second order elliptic equations, boundary value problems
35B25 Singular perturbations (PDE)
35C20 Asymptotic expansions of solutions of PDE

Keywords: convection-diffusion problems; singularly perturbed equation; asymptotic expansion

Highlights
Master Server

### Zentralblatt MATH Berlin [Germany]

© FIZ Karlsruhe GmbH

Zentralblatt MATH master server is maintained by the Editorial Office in Berlin, Section Mathematics and Computer Science of FIZ Karlsruhe and is updated daily.

Other Mirror Sites

Copyright © 2013 Zentralblatt MATH | European Mathematical Society | FIZ Karlsruhe | Heidelberg Academy of Sciences