Two-scale convergence in thin domains with locally periodic rapidly\n oscillating boundary

2017/03/27 by Irina Pettersson, Pettersson, Irina · 1 citation
Computer Science · Mathematics · #35B27 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1703.09027

openalex publication_date 2017/03/27 · openalex created_date 2022/08/06 · openalex updated_date 2026/07/28

Abstract

The aim of this paper is to adapt the notion of two-scale convergence in\nL^p to the case of a measure converging to a singular one. We present a\nspecific case when a thin cylinder with locally periodic rapidly oscillating\nboundary shrinks to a segment, and the corresponding measure charging the\ncylinder converges to a one-dimensional Lebegues measure of an interval. The\nmethod is then applied to the asymptotic analysis of linear elliptic operators\nwith locally periodic coefficients in a thin cylinder with locally periodic\nrapidly varying thickness.\n

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