Homogenization in a thin domain with an oscillatory boundary

Details Homogenization in a thin domain with an oscillatory boundary Homogenization in a thin domain with an oscillatory boundary

2011-01-18

arxiv.org/abs/1101.3503v1

Mathematics

Analysis of PDEs

27 pages, 2 figures

Scientific paper

In this paper we analyze the behavior of the Laplace operator with Neumann boundary conditions in a thin domain of the type $R^\epsilon = \{(x,y) \in \R^2; x \in (0,1), 0 < y < \epsilon G(x, x/\epsilon)\} $ where the function G(x,y) is periodic in y of period L. Observe that the upper boundary of the thin domain presents a highly oscillatory behavior and, moreover, the height of the thin domain, the amplitude and period of the oscillations are all of the same order, given by the small parameter $\epsilon$.

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