Loading [MathJax]/jax/output/SVG/jax.js
Search Advanced

Networks and Heterogeneous Media

2008, Volume 3, Issue 1: 97-124. doi: 10.3934/nhm.2008.3.97
Previous Article Next Article

Homogenization and correctors for the wave equation in non periodic perforated domains

  • 1.
    Laboratoire de Mathématiques Raphaël Salem, UMR CNRS 6085, Avenue de l’Université, BP 12, 76801 Saint Etienne de Rouvray
  • 2.
    Laboratoire Jacques-Louis Lions, UMR CNRS 7598, Université Paris 6 BP 187, 4 Place Jussieu 75252 Paris Cedex 05
  • Received: 01 May 2007 Revised: 01 October 2007

  • Primary: 35B27; Secondary: 35L05.

  • We consider here the wave equation in a (not necessarily periodic) perforated domain, with a Neumann condition on the boundary of the holes. Assuming H0-convergence ([3]) on the elliptic part of the operator, we prove two main theorems: a convergence result and a corrector one. To prove the corrector result, we make use of a suitable family of elliptic local correctors given in [4] whose columns are piecewise locally square integrable gradients. As in the case without holes ([2]), some additional assumptions on the data are needed.

    Citation: Patrizia Donato, Florian Gaveau. Homogenization and correctors for the wave equation in non periodic perforated domains[J]. Networks and Heterogeneous Media, 2008, 3(1): 97-124. doi: 10.3934/nhm.2008.3.97

    Related Papers:

    [1] Patrizia Donato, Florian Gaveau . Homogenization and correctors for the wave equation in non periodic perforated domains. Networks and Heterogeneous Media, 2008, 3(1): 97-124. doi: 10.3934/nhm.2008.3.97
    [2] Grigor Nika, Adrian Muntean . Hypertemperature effects in heterogeneous media and thermal flux at small-length scales. Networks and Heterogeneous Media, 2023, 18(3): 1207-1225. doi: 10.3934/nhm.2023052
    [3] Patrizia Donato, Olivier Guibé, Alip Oropeza . Corrector results for a class of elliptic problems with nonlinear Robin conditions and $ L^1 $ data. Networks and Heterogeneous Media, 2023, 18(3): 1236-1259. doi: 10.3934/nhm.2023054
    [4] Mogtaba Mohammed, Mamadou Sango . Homogenization of nonlinear hyperbolic stochastic partial differential equations with nonlinear damping and forcing. Networks and Heterogeneous Media, 2019, 14(2): 341-369. doi: 10.3934/nhm.2019014
    [5] Rémi Goudey . A periodic homogenization problem with defects rare at infinity. Networks and Heterogeneous Media, 2022, 17(4): 547-592. doi: 10.3934/nhm.2022014
    [6] Junlong Chen, Yanbin Tang . Homogenization of nonlinear nonlocal diffusion equation with periodic and stationary structure. Networks and Heterogeneous Media, 2023, 18(3): 1118-1177. doi: 10.3934/nhm.2023049
    [7] Ben Schweizer, Marco Veneroni . The needle problem approach to non-periodic homogenization. Networks and Heterogeneous Media, 2011, 6(4): 755-781. doi: 10.3934/nhm.2011.6.755
    [8] Renata Bunoiu, Claudia Timofte . Homogenization of a thermal problem with flux jump. Networks and Heterogeneous Media, 2016, 11(4): 545-562. doi: 10.3934/nhm.2016009
    [9] Hakima Bessaih, Yalchin Efendiev, Florin Maris . Homogenization of the evolution Stokes equation in a perforated domain with a stochastic Fourier boundary condition. Networks and Heterogeneous Media, 2015, 10(2): 343-367. doi: 10.3934/nhm.2015.10.343
    [10] Hiroshi Matano, Ken-Ichi Nakamura, Bendong Lou . Periodic traveling waves in a two-dimensional cylinder with saw-toothed boundary and their homogenization limit. Networks and Heterogeneous Media, 2006, 1(4): 537-568. doi: 10.3934/nhm.2006.1.537
  • We consider here the wave equation in a (not necessarily periodic) perforated domain, with a Neumann condition on the boundary of the holes. Assuming H0-convergence ([3]) on the elliptic part of the operator, we prove two main theorems: a convergence result and a corrector one. To prove the corrector result, we make use of a suitable family of elliptic local correctors given in [4] whose columns are piecewise locally square integrable gradients. As in the case without holes ([2]), some additional assumptions on the data are needed.


  • This article has been cited by:

    1. Mourad Sini, Haibing Wang, Qingyun Yao, Analysis of the Acoustic Waves Reflected by a Cluster of Small Holes in the Time-Domain and the Equivalent Mass Density, 2021, 19, 1540-3459, 1083, 10.1137/20M1319693
    2. Qiao-Li Dong, Li-Qun Cao, Multiscale asymptotic expansions methods and numerical algorithms for the wave equations in perforated domains, 2014, 232, 00963003, 872, 10.1016/j.amc.2013.12.112
    3. Mogtaba Mohammed, Mamadou Sango, Homogenization of Neumann problem for hyperbolic stochastic partial differential equations in perforated domains, 2016, 97, 18758576, 301, 10.3233/ASY-151355
  • Reader Comments
  • © 2008 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
Networks and Heterogeneous Media
1.2 1.8

Metrics

Article views(3847) PDF downloads(124) Cited by(3)

Preview PDF
Download XML
Export Citation
Article outline
Abstract

Other Articles By Authors

Related pages

Tools

Copyright © AIMS Press

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog