Comptes Rendus
no. 5
A high-order corrector estimate for a semi-linear elliptic system in perforated domains
Vo Anh Khoa1
1 Mathematics and Computer Science Division, Gran Sasso Science Institute, L'Aquila, Italy
Comptes Rendus. Mécanique, Volume 345 (2017) no. 5, pp. 337-343.

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].

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2017.03.003
Mots clés : Corrector estimate, Homogenization, Elliptic systems, Perforated domains
Vo Anh Khoa 1

1 Mathematics and Computer Science Division, Gran Sasso Science Institute, L'Aquila, Italy 
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Vo Anh Khoa. A high-order corrector estimate for a semi-linear elliptic system in perforated domains. Comptes Rendus. Mécanique, Volume 345 (2017) no. 5, pp. 337-343. doi : 10.1016/j.crme.2017.03.003. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2017.03.003/

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