Zeitschrift für Analysis und ihre Anwendungen
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Published online: 2001-12-31
Boundary Layer Correctors for the Solution of Laplace Equation in a Domain with Oscillating BoundaryY. Amirat and O. Bodart (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