Comportement asymptotique à haute conductivité de l'épaisseur de peau en électromagnétisme

Abstract: We study a three-dimensional model for the skin effect in electromagnetism. We first give a multiscale asymptotic expansion for the solution of the harmonic Maxwell equations set on a domain made of two materials, dielectric and highly conducting, with a regular interface between them. To measure the skin effect, we introduce a suitable skin depth function defined on the interface and generalizing the classical scalar quantity. We then prove an asymptotic expansion at high conductivity for this function, which exhibits the influence of the geometry of the interface on the skin depth. [Copyright &y& Elsevier]