Approximate transmission conditions through a weakly oscillating thin layer

摘要

We Study the behavior of the electro-quasistatic voltage potentials in a material composed by a bidimensional medium surrounded by a weakly oscillating thin layer and embedded in an ambient medium. We build approximate transmission conditions in order to replace the layer by these conditions on the boundary of the interior material. We deal with a weakly oscillating thin layer: the period of the oscillations is greater than the square root of the thinness. Our approach is essentially geometric and based on a suitable change of variable in the layer. This paper extends previous works (Methodes asymptotiques pour le calcul de champs electromagnetiques dans des milieux a couche mince. Application aux cellules biologiques. Thesis, Universite Lyon I. France, November 2006: IEEE Trans. Magn. 2007. http://hal.archives-ouvertes.fr/hal-00165049/fr.) of the former author, in which the layer had constant thickness. Copyright (C) 2008 John Wiley & Sons, Ltd.