Localization effect for a spectral problem in a perforated domain with Fourier boundary cconditions

2012/11/16 by Valeria Chiado Piat, Valeria Chiadò Piat, Iryna Pankratova +4 · 1 citation
Computer Science · Engineering · Mathematics · Physics and Astronomy · #35B27 #76M45 #78M35 #78M40 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory (math.SP) #math-ph #math.AP #math.MP #math.SP #msc:35B27 #msc:76M45 #msc:78M35 #msc:78M40

paper · pdf · doi:10.48550/arxiv.1211.3899

arxiv created 2012/11/16 · openalex publication_date 2012/11/16 · arxiv updated 2012/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a homogenization of elliptic spectral problem stated in a perforated domain, Fourier boundary conditions being imposed on the boundary of perforation. The presence of a locally periodic coefficient in the boundary operator gives rise to the effect of a localization of the eigenfunctions. Moreover, the limit behaviour of the lower part of the spectrum can be described in terms of an auxiliary harmonic oscillator operator. We describe the asymptotics of the eigenpairs and derive the estimates for the rate of convergence.

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