A two-scale model for the periodic homogenization of the wave equation

被引：12

作者：

Brassart, Matthieu ^{[1
]}

Lenczner, Michel ^{[2
]}

机构：

[1] Lab Math Besancon, F-25030 Besancon, France

[2] FEMTO ST, F-25000 Besancon, France

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2010年 / 93卷 / 05期

关键词：

Homogenization; Wave equation; Bloch waves; Two-scale convergence; SPECTRAL ASYMPTOTIC ANALYSIS; CONVERGENCE;

D O I：

10.1016/j.matpur.2010.01.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a new mathematical object designed to analyze the oscillations occurring on both microscopic and macroscopic scales in a wave equation with oscillating coefficients and data. Through a Bloch wave homogenization method, our study addresses typical problems of two-scale convergence in the interior of the domain, and sheds some light on the behavior near the boundary. A decoupled system of (systems of) transport equations is derived in each energy band, and the total energy field is approximated. We also recover previously known results in homogenization as a restricted part of our model. (C) 2010 Elsevier Masson SAS. All rights reserved.

引用

页码：474 / 517

页数：44

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