Homogenization in general periodically perforated domains by a spectral approach |
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Authors: | Marc Briane |
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Institution: | Centre de Mathématiques I.N.S.A. de Rennes & I.R.M.A.R., 20, avenue des Buttes de Co?smes, 35 043 Rennes Cedex, France (e-mail: mbriane@insa-rennes.fr), FR
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Abstract: | In this article we study the asymptotic behaviour as tends to 0 of the Neumann problem $-\Delta u_\epsilon+u_\epsilon=\epsilon$-periodic bounded open set of . The period cell of is equal to where is a regular open subset of the d-dimensional torus. We prove that if there exists a smallest integer such that the n-th non-zero eigenvalue of the spectral problem in satisfies , the limiting problem is a linear system of second order p.d.e.'s, of size n. By this spectral approach we extend in the periodic framework a result due to Khruslov without making strong geometrical
assumptions on the perforated domain .
Received: 20 December 2000 / Accepted: 11 May 2001 / Published online: 19 October 2001 |
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Keywords: | Mathematics Subject Classification (2000): 35B27 35J25 74Q15 76M50 |
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