We study the asymptotic behaviour of the inductance coefficient for a thin toroidal inductor whose thickness depends on a small parameter $\eps>0$. We give an explicit form of the singular part of the corresponding potential $u\ue$ which allows to construct the limit potential $u$ (as $\eps\to 0$) and an approximation of the inductance coefficient $L\ue$. We establish some estimates of the deviation $u\ue-u$ and of the error of approximation of the inductance. We show that $L\ue$ behaves asymptotically as $\ln\eps$, when $\eps\to 0$.
Publié le : 2002-07-05
Classification:
Asymptotic behavior,
self inductance,
eddy currents,
thin domain,
35B40 35Q60,
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
@article{hal-00086528,
author = {Amirat, Youcef and Touzani, Rachid},
title = {Asymptotic behaviour of the inductance coefficient for thin conductors},
journal = {HAL},
volume = {2002},
number = {0},
year = {2002},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00086528}
}
Amirat, Youcef; Touzani, Rachid. Asymptotic behaviour of the inductance coefficient for thin conductors. HAL, Tome 2002 (2002) no. 0, . http://gdmltest.u-ga.fr/item/hal-00086528/