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Homogenization of eigenvalue problems in perforated domains

  • M. Vanninathan
Article

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: λε = ε−2 λ + λ0 +O (ε), Stekloff: λε = ελ1 +O2), Neumann: λε = λ0 + ελ1 +O2).

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.

Keywords

Homogenization correctors eigenvalues eigenvectors 

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Copyright information

© Indian Academy of Sciences 1981

Authors and Affiliations

  • M. Vanninathan
    • 1
  1. 1.TIFR CentreIndian Institute of ScienceBangaloreIndia

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