Homogenization of Reticulated Structures

Abstract

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

“…As main tool, we follow the standard approach by the energy-like method to investigate the error estimate between the micro and macro concentrations and micro and macro concentration gradients. This work aims at generalizing the results reported in [2,7]. …”

“…It is worth noting that the following errors have been so far obtained for the homogenization of the above-mentioned microscopic elliptic system in [7] and further in [2]:…”

Corrector results for a parabolic problem with a memory effect

“…Our results can be related to the case of parabolic problems in perforated domains that were studied by Donato and Nabil [15]. The homogenization of Neumann boundary problems in perforated domains were investigated by Cioranescu and Saint Jean Paulin in [9,10]. For associated correctors we refer to Donato et al [16].…”

Some Mathematical Problems in Visual Transduction

“…A variant of an argument known in the theory of homogenization of stratified structures, yields ξ ≡ 0 (see [3], [7]). Therefore, taking the limit ε → 0 in (4.8) gives…”