2021/08/17 by Thuyen Dang, Dang, Thuyen, Yuliya Gorb +4
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #math.AP
paper · pdf · doi:10.48550/arxiv.2108.07775
24 pages, 2 figures, accepted version
openalex publication_date 2021/08/17 · openalex created_date 2021/08/30 · arxiv created 2022/02/11 · arxiv updated 2022/02/15 · openalex updated_date 2026/07/28
This paper generalizes the results obtained by the authors in \citedangHomogenizationNondiluteSuspension2021 concerning the homogenization of a non-dilute suspension of magnetic particles in a viscous flow. More specifically, in this paper, a restrictive assumption on the coefficients of the coupled equation, made in \citedangHomogenizationNondiluteSuspension2021, that significantly narrowed the applicability of the homogenization results obtained, is relaxed and a new regularity of the solution of the fine-scale problem is proven. In particular, we obtain a global L∞-bound for the gradient of the solution of the scalar equation -div [ a ( x/ε )∇ φε(x) ] = f(x), uniform with respect to microstructure scale parameter ε≪ 1 in a small interval (0,ε0), where the coefficient a is only piecewise Hölder continuous. Thenceforth, this regularity is used in the derivation of the effective response of the given suspension discussed in \citedangHomogenizationNondiluteSuspension2021.