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Homogenization of eigenvalue problems in perforated domains

Vanninathan, M (1981) Homogenization of eigenvalue problems in perforated domains. In: Proceedings Mathematical Sciences, 90 (3). pp. 239-271.

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In this paper, we treat some eigenvalue problems in periodically perforated domains and study the asymptotic behaviour of the eigenvalues and the eigenvectors when the number of holes in the domain increases to infinity Using the method of asymptotic expansion, we give explicit formula for the homogenized coefficients and expansion for eigenvalues and eigenvectors. If we denote by ε the size of each hole in the domain, then we obtain the following aysmptotic expansion for the eigenvalues: Dirichlet: λε = ε−2 λ + λ0 +O (ε), Stekloff: λε = ελ1 +O (ε2), Neumann: λε = λ0 + ελ1 +O (ε2).Using the method of energy, we prove a theorem of convergence in each case considered here. We briefly study correctors in the case of Neumann eigenvalue problem.

Item Type: Journal Article
Publication: Proceedings Mathematical Sciences
Publisher: Indian Academy of Sciences
Additional Information: Copyright of this article belongs to Indian Academy of Sciences.
Keywords: Homogenization;correctors;eigenvalues;eigenvectors
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 23 Feb 2012 05:19
Last Modified: 12 Oct 2018 08:04
URI: http://eprints.iisc.ac.in/id/eprint/43223

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