Article Dans Une Revue SIAM Journal on Mathematical Analysis Année : 2025

Uniform estimates for transmission problems in electromagnetism with high contrast in magnetic permeabilities

Résumé

We consider the time-harmonic Maxwell equations set on a domain made up of two subdomains that represent a magnetic conductor and a non-magnetic material, and we assume that the relative magnetic permeability $\mu_{r}$ between the two materials is high. We prove uniform a priori estimates for Maxwell solutions when the interface between the two subdomains is supposed to be Lipschitz. Assuming smoothness for the interface between the subdomains, we prove also that the magnetic field possesses a multiscale expansion in powers of $1/ \sqrt{\mu_{r}}$ with profiles rapidly decaying inside the magnetic conductor.

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Dates et versions

hal-04620526 , version 1 (21-06-2024)

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Victor Péron. Uniform estimates for transmission problems in electromagnetism with high contrast in magnetic permeabilities. SIAM Journal on Mathematical Analysis, 2025, 57 (6), pp.6072-6088. ⟨10.1137/24M1674601⟩. ⟨hal-04620526⟩
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