Homogenization of the Poisson equation in a non-periodically perforated domain
Keyword(s):
We study the Poisson equation in a perforated domain with homogeneous Dirichlet boundary conditions. The size of the perforations is denoted by ε > 0, and is proportional to the distance between neighbouring perforations. In the periodic case, the homogenized problem (obtained in the limit ε → 0) is well understood (see (Rocky Mountain J. Math. 10 (1980) 125–140)). We extend these results to a non-periodic case which is defined as a localized deformation of the periodic setting. We propose geometric assumptions that make precise this setting, and we prove results which extend those of the periodic case: existence of a corrector, convergence to the homogenized problem, and two-scale expansion.
2005 ◽
Vol 202
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pp. 488-506
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1984 ◽
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pp. 137-149
2013 ◽
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pp. 527-533
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2011 ◽
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pp. 1279-1294
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2016 ◽
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pp. 1843-1860
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pp. 59-69
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