A high-order corrector estimate for a semi-linear elliptic system in perforated domains

We derive in this Note a high-order corrector estimate for the homogenization of a microscopic semi-linear elliptic system posed in perforated domains. The major challenges are the presence of nonlinear volume and surface reaction rates. This type of correctors justifies mathematically the convergen...

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Bibliographic Details
Published inComptes rendus. Mecanique Vol. 345; no. 5; pp. 337 - 343
Main Author Khoa, Vo Anh
Format Journal Article
LanguageEnglish
Published Elsevier Masson SAS 01.05.2017
Subjects
Corrector estimate
Elliptic systems
Homogenization
Perforated domains
Homogenization
Elliptic systems
Perforated domains
Corrector estimate
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Summary:We derive in this Note a high-order corrector estimate for the homogenization of a microscopic semi-linear elliptic system posed in perforated domains. The major challenges are the presence of nonlinear volume and surface reaction rates. This type of correctors justifies mathematically the convergence rate of formal asymptotic expansions for the two-scale homogenization settings. As the main tool, we use energy-like estimates to investigate the error estimate between the micro and macro concentrations and between the corresponding micro- and macro-concentration gradients. This work aims at generalizing the results reported in [1,2].
ISSN:1631-0721
1873-7234
1873-7234
DOI:10.1016/j.crme.2017.03.003