Analysis of integral equations attached to skin effect

Vrkoč, Ivo

doi:10.21136/AM.1985.104163

Geodesic

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Analysis of integral equations attached to skin effect

Vrkoč, Ivo

Applications of Mathematics, Tome 30 (1985) no. 5, pp. 361-374.

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Résumé

The paper is a mathematical background of the paper of D. Mayer, B. Ulrych where the mathematical model of the skin effect is established and discussed. It is assumed that the currents passing through parallel conductors are under effect of a variable magnetic field. The phasors of the density of the current are solutions of

f (x) - j q \sum_{i = 1}^{k} b_{i} \int_{S i} f (y) V (| y - x |) d y - c_{p} = h (x)

for

x \in S_{p}, p = 1, \dots, k

\int_{S i} f (x) d x = I_{i}, i = 1, \dots, k

, where

j

is the imaginary unit,

b_{i}, q, I_{i}

are given constants, #h(x)

i s a g i v e n f u n c t i o n a n d

f(x)

i s a n u n k n o w n f u n c t i o n a n d

c_i$ are unknown constants. The first and the second section of this paper are devoted to the problem of existence and unicity of a solution. The third section is devoted to a numerical method.

MR Zbl

DOI : 10.21136/AM.1985.104163

Classification : 45H05, 45L10, 65R20, 78A30, 78A55
Mots-clés : quadrature formula method; surface phenomenon; skin effect; existence; uniqueness

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     title = {Analysis of integral equations attached to skin effect},
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     language = {en},
     url = {https://geodesic-test.mathdoc.fr/articles/10.21136/AM.1985.104163/}
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Vrkoč, Ivo. Analysis of integral equations attached to skin effect. Applications of Mathematics, Tome 30 (1985) no. 5, pp. 361-374. doi : 10.21136/AM.1985.104163. https://geodesic-test.mathdoc.fr/articles/10.21136/AM.1985.104163/

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