Geodesic
Solution behaviour of non-linear magnetostatic problem around ferromagnetic's corner point
Matematičeskoe modelirovanie, Tome 15 (2003) no. 4, pp. 77-84.

Voir la notice de l'article provenant de la source Math-Net.Ru

A non-linear boundary value problem was studied in a corner domain. This problem aroze from seeking for the distribution of magnetic field. Numerical methods are usually used to solve such a problem, therefore it was important to study the solutions smoothness around a corner point. Non-linear problems in this aspect are not studied enough. However, simular investigations were performed for linear problems. In one of our previous papers we considered a quasi-linear magnetostatic problem. In this paper we consider a case of non-linear boundary-value magnetostatic problem and give the proof of the theorem about finiteness around a corner point. 
@article{MM_2003_15_4_a5,
     author = {E. P. Zhidkov and E. E. Perepelkin},
     title = {Solution behaviour of non-linear magnetostatic problem around ferromagnetic's corner point},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {77--84},
     publisher = {mathdoc},
     volume = {15},
     number = {4},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2003_15_4_a5/}
}
TY  - JOUR
AU  - E. P. Zhidkov
AU  - E. E. Perepelkin
TI  - Solution behaviour of non-linear magnetostatic problem around ferromagnetic's corner point
JO  - Matematičeskoe modelirovanie
PY  - 2003
SP  - 77
EP  - 84
VL  - 15
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2003_15_4_a5/
LA  - ru
ID  - MM_2003_15_4_a5
ER  - 
%0 Journal Article
%A E. P. Zhidkov
%A E. E. Perepelkin
%T Solution behaviour of non-linear magnetostatic problem around ferromagnetic's corner point
%J Matematičeskoe modelirovanie
%D 2003
%P 77-84
%V 15
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2003_15_4_a5/
%G ru
%F MM_2003_15_4_a5
E. P. Zhidkov; E. E. Perepelkin. Solution behaviour of non-linear magnetostatic problem around ferromagnetic's corner point. Matematičeskoe modelirovanie, Tome 15 (2003) no. 4, pp. 77-84. http://geodesic.mathdoc.fr/item/MM_2003_15_4_a5/

[1] L. A. Oganesyan, V. Ya. Rivkind, L. A. Rukhovets, Trudy seminara differentsialnye uravneniya i ikh primenenie, Ch. 2, vyp. 8, Vilnyus, 1974

[2] V. A. Kondratev, Trudy moskovskogo matematicheskogo obschestva, 16 (1967), 209–292 | MR

[3] I. V. Fryazinov, ZhVMiMF, 18:5 (1978), 1171–1185 | MR

[4] E. P. Zhidkov, E. E. Perepelkin, Kraevaya zadacha dlya uravneniya ellipticheskogo tipa v oblasti s uglom, R5-2000-52, OIYaI, Dubna | MR

[5] E. P. Zhidkov, E. E. Perepelkin, “An analytical approach for quasi-linear equation in second order”, CMAM, 1:3 (2001), 285–297 | MR | Zbl

[6] P. Kurant, Uravneniya s chastnymi proizvodnymi, T. 2, Mir, M., 1964 | MR