2014/07/14 by Mariya Ptashnyk, Ptashnyk, Mariya · 2 citations
Computer Science · Engineering · Mathematics · #35B27 #35D30 #35Kxx #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Composite Material Mechanics #Differential Equations and Numerical Methods #FOS: Mathematics #math.AP #msc:35B27 #msc:35D30 #msc:35Kxx
paper · pdf · doi:10.48550/arxiv.1407.3821
openalex publication_date 2014/07/14 · arxiv created 2015/09/20 · arxiv updated 2015/09/22 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
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.