Geodesic
Constructing solutions to systems of nonlinear equations for magnetic insulation modelling
Sibirskij žurnal industrialʹnoj matematiki, Tome 18 (2015) no. 1, pp. 69-83.

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

We consider a model of magnetic insulation in a plane diode which is presented as a system of two nonlinear second-order ODE. Integrability of the model is justified and a method for solving a singular boundary value problem is developed. We propose a generalized model of magnetic insulation with multidimensional Laplace operator, which is the principal object of study in this paper. We obtain conditions under which exact solutions to the boundary value problem for a spherical layer are found.
Keywords: singular boundary value problem, integrability
Mots-clés : elliptic type equation, exact solution. 
@article{SJIM_2015_18_1_a5,
     author = {A. A. Kosov and E. I. Semenov and A. V. Sinitsyn},
     title = {Constructing solutions to systems of nonlinear equations for magnetic insulation modelling},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {69--83},
     publisher = {mathdoc},
     volume = {18},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2015_18_1_a5/}
}
TY  - JOUR
AU  - A. A. Kosov
AU  - E. I. Semenov
AU  - A. V. Sinitsyn
TI  - Constructing solutions to systems of nonlinear equations for magnetic insulation modelling
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2015
SP  - 69
EP  - 83
VL  - 18
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2015_18_1_a5/
LA  - ru
ID  - SJIM_2015_18_1_a5
ER  - 
%0 Journal Article
%A A. A. Kosov
%A E. I. Semenov
%A A. V. Sinitsyn
%T Constructing solutions to systems of nonlinear equations for magnetic insulation modelling
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2015
%P 69-83
%V 18
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2015_18_1_a5/
%G ru
%F SJIM_2015_18_1_a5
A. A. Kosov; E. I. Semenov; A. V. Sinitsyn. Constructing solutions to systems of nonlinear equations for magnetic insulation modelling. Sibirskij žurnal industrialʹnoj matematiki, Tome 18 (2015) no. 1, pp. 69-83. http://geodesic.mathdoc.fr/item/SJIM_2015_18_1_a5/

[1] Ben Abdallah N., Degond P., Mehats F., “Mathematical model of magnetic insulation”, Physics of plasmas, 5 (1998), 1522–1534 | DOI | MR

[2] Sinitsyn A. V., “Polozhitelnye resheniya nelineinoi singulyarnoi kraevoi zadachi magnitnoi izolyatsii”, Mat. modelirovanie, 13:5 (2001), 37–52 | MR | Zbl

[3] Semenov E. I., Sinitsyn A. V., “Matematicheskaya model magnitnoi izolyatsii vakuumnogo dioda i ee tochnye resheniya”, Izv. IGU. Ser. Matematika, 2010, no. 1, 78–91

[4] Kosov A. A., Sinitsyn A. V., “O postroenii pervykh integralov dlya odnogo klassa nelineinykh sistem”, Izv. IGU. Ser. Matematika, 2012, no. 1, 57–69 | Zbl

[5] Varin V. P., “An analysis of a vacuum diode model”, Comput. Math. Math. Phys., 53:2 (2013), 194–204 | DOI | MR | Zbl

[6] Polyanin A. D., Zaitsev V. F., Spravochnik po nelineinym uravneniyam matematicheskoi fiziki. Tochnye resheniya, Fizmatlit, M., 2002 | MR

[7] Pukhnachev V. V., “Tochnye resheniya uravnenii dvizheniya neszhimaemoi vyazkouprugoi sredy Maksvella”, Prikl. mekhanika i tekhn. fizika, 50:2 (2009), 16–23 | MR

[8] Vyazmina E. A., Polyanin A. D., “Novye klassy tochnykh reshenii nelineinykh diffuzionno-kineticheskikh uravnenii i sistem obschego vida”, Teor. osnovy khim. tekhnologii, 40:6 (2006), 1–10

[9] Andreev V. K., Kaptsov O. V., Pukhnachev V. V., Rodionov A. A., Primenenie teoretiko-gruppovykh metodov v gidrodinamike, Nauka, Novosibirsk, 1994 | MR | Zbl

[10] Uitteker E. T., Analiticheskaya dinamika, izd. Udmurt. un-ta, Izhevsk, 1999

[11] Babich V. M., Kapilevich M. B., Mikhlin S. G. i dr., Lineinye uravneniya matematicheskoi fiziki, Nauka, M., 1964 | MR | Zbl

[12] Polyanin A. D., Nelineinye sistemy dvukh differentsialnykh uravnenii v chastnykh proizvodnykh, URL: http://eqworld.ipmnet.ru/ru/solutions/syspde/spde-toc3.htm

[13] Tikhonov A. N., Samarskii A. A., Uravneniya matematicheskoi fiziki, Nauka, M., 1977