Locally periodic thin domains with varying period.

Abstract

Analizamos el comportamiento de las soluciones de las ecuación de Laplace con condiciones de frontera Neumann en un dominio fino con una frontera oscilante. Las oscilaciones son localmente periódicas en el sentido de que la amplitud y el periodo de las oscilaciones puede no ser constante

We analyze the behavior of the solutions of the Laplace equation with Neumann boundary conditions in a thin domain with a highly oscillatory behavior. The oscillations are locally periodic in the sense that both the amplitude and the period of the oscillations may not be constant and actually they vary in space. We obtain the asymptotic homogenized limit and provide some correctors. To accomplish this goal, we extend the unfolding operator method to the locally periodic case. The main ideas of this extension may be applied to other cases like perforated domains or reticulated structures, which are locally periodic with not necessarily a constant period.