We study the asymptotic behavior of the solution of the Laplace equation in a domain, a part of whose boundary is highly oscillating. The motivation comes from the study of a longitudinal flow in an infinite horizontal domain bounded at the bottom by a wall and at the top by a rugose wall. The latter is a plane covered with periodic asperities whose size depends on a small parameter, ε > 0. The assumption of sharp asperities is made; that is, the height of the asperities is fixed. Using a boundary layer corrector, we derive and analyze a nonoscillating approximation of the solution at order O(ε^(3⁄2)) for the H^1-norm.
ASYMPTOTIC APPROXIMATION OF THE SOLUTION OF THE LAPLACE EQUATION IN A DOMAIN WITH HIGHLY OSCILLATING BOUNDARY / Amirat, Y.; Bodart, O.; DE MAIO, Umberto; Gaudiello, A.. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - (2004), pp. 1598-1616.
ASYMPTOTIC APPROXIMATION OF THE SOLUTION OF THE LAPLACE EQUATION IN A DOMAIN WITH HIGHLY OSCILLATING BOUNDARY
DE MAIO, UMBERTO;A. GAUDIELLO
2004
Abstract
We study the asymptotic behavior of the solution of the Laplace equation in a domain, a part of whose boundary is highly oscillating. The motivation comes from the study of a longitudinal flow in an infinite horizontal domain bounded at the bottom by a wall and at the top by a rugose wall. The latter is a plane covered with periodic asperities whose size depends on a small parameter, ε > 0. The assumption of sharp asperities is made; that is, the height of the asperities is fixed. Using a boundary layer corrector, we derive and analyze a nonoscillating approximation of the solution at order O(ε^(3⁄2)) for the H^1-norm.| File | Dimensione | Formato | |
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