Geodesic
One approach to a magnetostatic problem for bodies with inclusions in an inhomogeneous external field
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 1, pp. 178-188 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A direct magnetostatic problem for magnets with a finite-size inclusion is considered in an integrodifferential form. An approach is used that, under certain conditions, reduces the problem to a single integral equation on a two-dimensional manifold-the inclusion surface. As an important illustrative example, finite formulas are derived to compute the resulting field of a magnetic half-space with a spherical cavity in an arbitrary external field. 
@article{ZVMMF_2009_49_1_a11,
     author = {V. V. Dyakin and V. Ya. Raevskii and O. V. Umergalina},
     title = {One approach to a magnetostatic problem for bodies with inclusions in an inhomogeneous external field},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {178--188},
     year = {2009},
     volume = {49},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_1_a11/}
}
TY  - JOUR
AU  - V. V. Dyakin
AU  - V. Ya. Raevskii
AU  - O. V. Umergalina
TI  - One approach to a magnetostatic problem for bodies with inclusions in an inhomogeneous external field
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2009
SP  - 178
EP  - 188
VL  - 49
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_1_a11/
LA  - ru
ID  - ZVMMF_2009_49_1_a11
ER  - 
%0 Journal Article
%A V. V. Dyakin
%A V. Ya. Raevskii
%A O. V. Umergalina
%T One approach to a magnetostatic problem for bodies with inclusions in an inhomogeneous external field
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2009
%P 178-188
%V 49
%N 1
%U http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_1_a11/
%G ru
%F ZVMMF_2009_49_1_a11
V. V. Dyakin; V. Ya. Raevskii; O. V. Umergalina. One approach to a magnetostatic problem for bodies with inclusions in an inhomogeneous external field. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 1, pp. 178-188. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_1_a11/

[1] Sapozhnikov A. B., Teoreticheskie osnovy elektromagnitnoi defektoskopii metallicheskikh tel, Izd-vo TGU, Tomsk, 1980

[2] Khizhnyak H. A., Integralnye uravneniya klassicheskoi elektrodinamiki, Nauk. dumka, Kiev, 1966

[3] Friedman M. J., “Mathematical study of the nonlinear singular integral magnetic field equation. 1”, SIAM. J. Appl. Math., 39:1 (1980), 14–20 | DOI | MR | Zbl

[4] Friedman M. J., “Mathematical study of the nonlinear singular integral magnetic field equation. 3”, SIAM. J. Appl. Math., 12:4 (1981), 536–540 | DOI | MR | Zbl

[5] Raevskii V. Ya., O svoistvakh kvaziermitovykh operatorov i ikh primenenii k issledovaniyu operatorov teorii potentsiala i osnovnogo uravneniya elektro- i magnitostatiki, Preprint No 24/48(01), IFM UrO RAN, Ekaterinburg, 2001

[6] Dyakin V. V., Umergalina O. V., “K raschetu polya defekta v trekhmernom poluprostranstve”, Defektoskopiya, 2003, no. 4, 52–66

[7] Varshalovich D. A., Moskaleva A. N., Khersonskii V. K., Kvantovaya teoriya uglovogo momenta, Nauka, L., 1975

[8] Kantorovich L. V., Akilov G. P., Funktsionalnyi analiz, Nauka, M., 1977 | MR | Zbl

[9] Dyakin V. V., Umergalina O. V., Raevskii V. Ya., “Pole konechnogo defekta v trekhmernom poluprostranstve”, Defektoskopiya, 2005, no. 8, 28—42

[10] Dyakin V. V., Raevskii V. Ya., Umergalina O. V., “Magnitostaticheskaya zadacha dlya poluprostranstva s sharovym defektom v neodnorodnom vneshnem pole”, Defektoskopiya, 2007, no. 1, 3–15 | MR