Homogenization for the Poisson equation in randomly perforated domains under minimal assumptions on the size of the holes
| Autor: | Richard M. Höfer, Arianna Giunti, Juan J. L. Velázquez |
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| Rok vydání: | 2018 |
| Předmět: |
Applied Mathematics
010102 general mathematics Mathematical analysis 01 natural sciences Homogenization (chemistry) 010101 applied mathematics Mathematics - Analysis of PDEs 35B27 35J15 35J57 60F15 60G55 Bounded function FOS: Mathematics 0101 mathematics Poisson's equation Analysis Mathematics Analysis of PDEs (math.AP) |
| DOI: | 10.48550/arxiv.1803.10214 |
| Popis: | This paper deals with the homogenization of the Poisson equation in a bounded domain of $\mathbb{R}^d$, $d>2$, which is perforated by a random number of small spherical holes with random radii and positions. We show that for a class of stationary short-range correlated measures for the centres and radii of the holes, we recover in the homogenized limit an averaged analogue of the "strange term" obtained by Cioranescu and Murat in the periodic case [D. Cioranescu and F. Murat, \textit{Un term ��trange venu d'ailleurs} (1986)]. We stress that we only require that the random radii have finite $(d-2)$-moment, which is the minimal assumption in order to ensure that the average of the capacity of the balls is finite. Under this assumption, there are holes which overlap with probability one. However, we show that homogenization occurs and that the clustering holes do not have any effect in the resulting homogenized equation. 35 pages |
| Databáze: | OpenAIRE |
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