Corrector for a diffusion process in a rarefied binary structure

Article type: Research Article

Authors: Nadia, Bengouga | Fadila, Bentalha^{; *}

Affiliations: Laboratory of Partial Differential Equations and Their Applications LEDPA, Faculty of Mathematics and Informatics, University of Batna 2, Batna, Algeria

Correspondence: [*] Corresponding author. E-mail: fbentalha@hotmail.com.

Abstract: The aim of this paper is to provide corrector results associated to the homogenization of a diffusion process which takes place in a binary structure formed by an ambiental connected phase surrounding a suspension of very small spheres distributed in a ε-periodic network. The suspension has a total mass of unity order and a vanishing volume. The results obtained here complete the earlier study by Bentalha et al. [Revue Roumaine de Math. Pures Appl. 52(2) (2007), 129–149] on the asymptotic behavior of this problem.

Keywords: diffusion, periodic homogenization, corrector, non-local effects, fine-scale substructure

DOI: 10.3233/ASY-161368

Journal: Asymptotic Analysis, vol. 98, no. 3, pp. 257-284, 2016