Increase of Dimension by Homogenization |
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Authors: | Briane Marc |
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Affiliation: | (1) Laboratoire L.A.N.S., I.N.S.A. de Rennes & I.R.M.A.R., 20, avenue des buttes de Coësmes, CS 14315, 35043 Rennes Cedex, France |
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Abstract: | The paper deals with the homogenization of a Neumann's problem in a thin periodic weakly connected domain of R3. The domain n is composed of a large number n of disjoint periodic connected components linked by a periodic lattice n of very thin bridges. According to the distribution and to the size of the linking bridges, the limit problem as n tends to infinity is either a 4d Neumann's problem or a 4d nonlocal problem. The additional term corresponding to the increase of dimension is due to the connection effect of the bridges. |
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Keywords: | effective equation homogenization multiscale problem Neumann problem periodic microstructure |
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