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Homogenization of Steklov Spectral Problems with Indefinite Density Function in Perforated Domains

Homogenization of Steklov Spectral Problems with Indefinite Density Function in Perforated Domains 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Homogenization of Steklov Spectral Problems with Indefinite Density Function in Perforated Domains

Acta Applicandae Mathematicae , Volume 123 (1) – Jun 14, 2012

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References (37)

Publisher
Springer Journals
Copyright
Copyright © 2012 by Springer Science+Business Media B.V.
Subject
Mathematics; Mathematics, general; Computer Science, general; Theoretical, Mathematical and Computational Physics; Statistical Physics, Dynamical Systems and Complexity; Mechanics
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/s10440-012-9765-4
Publisher site
See Article on Publisher Site

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.

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: Jun 14, 2012

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