Homogenization in a thin domain with an oscillatory boundary

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Abstract

In this paper we analyze the behavior of the Laplace operator with Neumann boundary conditions in a thin domain of the type Rε={(x1,x2)εR{double-struck}2|x1ε(0,1),0<x2<εG(x1,x1/ε)} 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 ε. © 2011 Elsevier Masson SAS.

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Arrieta, J. M., & Pereira, M. C. (2011). Homogenization in a thin domain with an oscillatory boundary. Journal Des Mathematiques Pures et Appliquees, 96(1), 29–57. https://doi.org/10.1016/j.matpur.2011.02.003

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