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Zeitschrift für Analysis und ihre Anwendungen


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Volume 20, Issue 4, 2001, pp. 929–940
DOI: 10.4171/ZAA/1052

Published online: 2001-12-31

Boundary Layer Correctors for the Solution of Laplace Equation in a Domain with Oscillating Boundary

Y. Amirat[1] and O. Bodart[2]

(1) Université Blaise Pascal, Aubière, France
(2) Université Blaise Pascal, Aubière Cedex, France

We study the asymptotic behaviour of the solution of Laplace equation in a domain with very rapidly oscillating boundary. The motivation comes from the study of a longitudinal flow in an infinite horizontal domain bounded at the bottom by a plane wall and at the top by a rugose wall. The rugose wall is a plane covered with periodic asperities which size depends on a small parameter $\epsilon > 0$. The assumption of sharp asperities is made, that is the height of the asperities does not vanish as $\epsilon \to 0$. We prove that, up to an exponentially decreasing error, the solution of Laplace equation can be approximated, outside a layer of width 2$\epsilon$, by a non-oscillating explicit function.

Keywords: Asymptotic behaviour, oscillating boundary, boundary layers

Amirat Y., Bodart O.: Boundary Layer Correctors for the Solution of Laplace Equation in a Domain with Oscillating Boundary. Z. Anal. Anwend. 20 (2001), 929-940. doi: 10.4171/ZAA/1052