Locally periodic unfolding method and two-scale convergence on surfaces of locally periodic microstructures
Abstract
In this paper we generalize the periodic unfolding method and the notion of two-scale convergence on surfaces of periodic microstructures to locally periodic situations. The methods that we introduce allow us to consider a wide range of non-periodic microstructures, especially to derive macroscopic equations for problems posed in domains with perforations distributed non-periodically. Using the methods of locally periodic two-scale convergence (l-t-s) on oscillating surfaces and the locally periodic (l-p) boundary unfolding operator, we are able to analyze differential equations defined on boundaries of non-periodic microstructures and consider non-homogeneous Neumann conditions on the boundaries of perforations, distributed non-periodically.
Keywords
Cite
@article{arxiv.1407.3821,
title = {Locally periodic unfolding method and two-scale convergence on surfaces of locally periodic microstructures},
author = {Mariya Ptashnyk},
journal= {arXiv preprint arXiv:1407.3821},
year = {2015}
}