Bloch waves homogenization of a Dirichlet problem in a periodically perforated domain

被引：3

作者：

Dupuy, Delphine ^{[3
]}

Orive, Rafael ^{[4
]}

Smaranda, Loredana ^{[1
,2
]}

机构：

[1] Univ Chile, Ctr Modelamiento Matemat, Santiago, Chile

[2] Univ Pitesti, Dept Math, Pitesti, Romania

[3] Ecole Natl Super Mines, Dept G2I 3MI, F-42023 St Etienne 2, France

[4] Univ Autonoma Madrid, Dept Matemat, E-28049 Madrid, Spain

来源：

ASYMPTOTIC ANALYSIS | 2009年 / 61卷 / 3-4期

关键词：

homogenization; perforated domains; Bloch waves; asymptotic behavior; APPROXIMATION;

D O I：

10.3233/ASY-2008-0912

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we use the spectral method of Bloch waves to study the homogenization process of the Poisson equation in a periodically perforated domain, under homogeneous Dirichlet conditions on both exterior and interior boundaries, as the hole size goes to zero more rapidly than the micro-structure size. Using this method, we find the exact value of the critical hole size, which separates the different behaviors, where the classical strange term may or may not appear in the homogenized equation. This strange term is related to the asymptotic behavior of the first eigenvalue with respect to the hole radius.

引用

页码：229 / 250

页数：22

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