Two-scale convergence of a class of r-forms: rewriting of periodic homogenization of Maxwell’s equations

Alphonse Mba (), Marcial Nguemfouo () and Hubert Nnang ()
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Alphonse Mba: University of Yaounde 1
Marcial Nguemfouo: University of Yaounde 1
Hubert Nnang: University of Yaounde 1

Partial Differential Equations and Applications, 2024, vol. 5, issue 3, 1-29

Abstract: 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 $$L^{1}$$ L 1 -coefficients defined on an open set $$\Omega $$ Ω of $${\mathbb {R}}^N$$ R N with $$r \in \{ 0, 1, \ldots , N \},$$ r ∈ { 0 , 1 , … , 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.

Keywords: Maxwell’s equations; Differential forms; Hodge- $$\star $$ ⋆ operator; Two-scale convergence; 35B27; 35B40; 35Q61; 58A10; 58A25 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s42985-024-00286-y

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