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Homogenization of Steklov spectral problems with indefinite density function in perforated domains

2011/06/20 by Hermann Douanla, Hermann Yonta Douanla, Douanla, Hermann Yonta · 1 citation
Computer Science · Engineering · Mathematics · Physics and Astronomy · #35B27 #35B40 #45C05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #math-ph #math.AP #math.MP #msc:35B27 #msc:35B40 #msc:45C05

paper · pdf · doi:10.48550/arxiv.1106.3904

24 pages. arXiv admin note: substantial text overlap with arXiv:1106.3907

openalex publication_date 2011/06/20 · arxiv created 2012/08/21 · arxiv updated 2012/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The asymptotic behavior of second order self-adjoint elliptic Steklov eigenvalue problems with periodic rapidly oscillating coefficients and with indefinite (sign-changing) density function is investigated in periodically perforated domains. We prove that the spectrum of this problem is discrete and consists of two sequences, one tending to -∞ and another to +∞. The limiting behavior of positive and negative eigencouples depends crucially on whether the average of the weight over the surface of the reference hole is positive, negative or equal to zero. By means of the two-scale convergence method, we investigate all three cases.

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