Homogenization in a thin domain with an oscillatory boundary

By José M. Arrieta, Marcone C. Pereira. 2011

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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 R ϵ = { ( x 1 , x 2 ) ∈ R 2 | x 1 ∈ ( 0 , 1 ) , 0 x 2 ϵ G ( x 1 , x 1 / 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.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/48df6850be5b4b99d40951ced8505e1de361b822