Vanninathan, M. (1981) Homogenization of eigenvalue problems in perforated domains Proceedings of the Indian Academy of Sciences  Mathematical Sciences, 90 (3). pp. 239271. ISSN 02534142

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Official URL: http://www.ias.ac.in/j_archive/mathsci/90/3/23927...
Related URL: http://dx.doi.org/10.1007/BF02838079
Abstract
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: λ_{ε}=ε^{−2}λ+λ_{0}+O (ε), Stekloff: λ_{ε}=_{ε}λ_{1}+O (ε^{2}), Neumann: λ_{ε}=λ_{0}+_{ε}λ_{1}+O (ε^{2}). 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:  Article 

Source:  Copyright of this article belongs to Indian Academy of Sciences. 
Keywords:  Homogenization; Correctors; Eigenvalues; Eigenvectors 
ID Code:  55288 
Deposited On:  18 Aug 2011 07:03 
Last Modified:  18 May 2016 07:37 
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