A Two-dimensional eddy current model using thin inductors

2006/07/11 by Youcef Amirat, Amirat, Youcef, Rachid Touzani +1
Mathematics · #35B40 35Q60 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35B40 #msc:35Q60

paper · pdf · doi:10.48550/arxiv.math/0607257

arxiv created 2006/07/11 · arxiv updated 2009/12/01

Abstract

We derive a mathematical model for eddy currents in two dimensional geometries where the conductors are thin domains. We assume that the current flows in the x_3-direction and the inductors are domains with small diameters of order O(ε). The model is derived by taking the limit ε→ 0. A convergence rate of O(ε^α) with 0<α<1/2 in the L²--norm is shown as well as weak convergence in the W^1,p spaces for 1< p <2.

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