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Explicit formulas for homogenization limits in certain non‐periodic problems including ramified domains
Author(s) -
Eberle Simon
Publication year - 2016
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201500207
Subject(s) - homogenization (climate) , mathematics , fractal , scaling limit , periodic boundary conditions , mathematical analysis , scaling , poisson distribution , limit (mathematics) , boundary value problem , statistical physics , physics , geometry , statistics , biodiversity , ecology , biology
In this paper we give an explicit formula for the homogenization limit of Poisson's equation for a wide range of non‐periodic 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.