Geodesic
Homogenization of the boundary-value problem for the biharmonic equation in a domain containing thin canals of small length
Sbornik. Mathematics, Tome 192 (2001) no. 10, pp. 1553-1585 Cet article a éte moissonné depuis la source Math-Net.Ru

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The present paper is devoted to homogenization of the boundary-value problem for the biharmonic equation in a planar domain containing thin canals of width $a_\varepsilon$ and of small length $\varepsilon^q$ $(q>0)$ situated $\varepsilon$-periodically along one of the coordinate axes. 
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     author = {T. A. Shaposhnikova},
     title = {Homogenization of the~boundary-value problem for the~biharmonic equation in a~domain containing thin canals of small length},
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     pages = {1553--1585},
     year = {2001},
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     url = {http://geodesic.mathdoc.fr/item/SM_2001_192_10_a7/}
}
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T. A. Shaposhnikova. Homogenization of the boundary-value problem for the biharmonic equation in a domain containing thin canals of small length. Sbornik. Mathematics, Tome 192 (2001) no. 10, pp. 1553-1585. http://geodesic.mathdoc.fr/item/SM_2001_192_10_a7/

[1] Marchenko V. A., Khruslov E. Ya., Kraevye zadachi v oblastyakh s melkozernistoi granitsei, Kiev, 1974

[2] Shaposhnikova T. A., “Ob usrednenii zadachi Neimana v oblasti, chast kotoroi predstavlyaet soboi sovokupnost kanalov”, Differents. uravneniya, 2001 (to appear)

[3] Oleinik O. A., Shaposhnikova T. A., “On the homogenization of the Poisson equation in partially perforated domains with arbitrary density of cavities and mixed type conditions on their boundary”, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., 7:3 (1996), 129–146 | MR | Zbl