Fast and slow boundary oscillations in a thin domain

Abstract

In this work we analyze the behavior of the solutions of the Laplace operator with Neumann boundary conditions in a 2-dimensional thin domain with order of thickness ε which presents a high oscillatory behavior at the top and a weak oscillatory behavior at the bottom boundary.We obtain the asymptotic homogenized problem as ε → 0 and we are interested in understanding how the extremely different order of the oscillations affects to the limit.