Explicit formulas for homogenization limits in certain non-periodic problems including ramified domains

In this paper we give an explicit formula for the homogenization limit of Poisson's equation for a wide range of nonperiodic problems including self-similarly ramified domains. This work was motivated by the modelling of the diffusion of medical sprays in lungs, which can be approximated by a self-similarly ramified domain. Such motivation also led us to consider the influence that a continuous scaling of the size of holes towards a chosen direction (e.g. towards the fractal boundary) has on the homogenization limit. It turned out that our strategy to explicitly calculate a formula for the homogenization limit could be applied beyond self-similar perforations as presented in this article. (C) 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim