Abstract
Periodic homogenization is studied for Maxwell’s equations with the linear conductivity. After generalizing the sequential compactness theorem of Nguetseng (SIAM J Math Anal 20:608–623, 1989), repeated to a sequence of r-differential forms of \(L^{1}\)-coefficients defined on an open set \(\Omega \) of \({\mathbb {R}}^N\) with \(r \in \{ 0, 1, \ldots , N \},\) it is shown that the sequence of solutions to a class of reduced system converges to the solution of a homogenized reduced Maxwell’s equations.
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The authors wish to thank particularly authors of [12] for their fantastic work which permits to simplify some fundamental results and computational operations of the present work. We thank the Editor and reviewers for their handling of the review process.
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Alphonse Mba, Marcial Nguemfouo and Hubert Nnang contributed equally to this work.
This article is part of the section “Theory of PDEs” edited by Eduardo Teixeira.
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Mba, A., Nguemfouo, M. & Nnang, H. Two-scale convergence of a class of r-forms: rewriting of periodic homogenization of Maxwell’s equations. Partial Differ. Equ. Appl. 5, 17 (2024). https://doi.org/10.1007/s42985-024-00286-y
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DOI: https://doi.org/10.1007/s42985-024-00286-y