Geodesic
On a family of steady-state distributions of the Vlasov–Maxwell–Fokker–Planck system
The Bulletin of Irkutsk State University. Series Mathematics, Tome 4 (2011) no. 3, pp. 124-131
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A family of distributions in the form of an exponential, which depends on a scalar function is constructed for the steady-state Vlasov–Maxwell–Fokker–Planck system. Through a scalar function defined relevant electromagnetic field. It is shown that solvability of the VMFP system for one-kind distribution function reduces to semilinear elliptic Liouville equation. We present some exact solutions of the last equation.
Mots-clés : Vlasov–Maxwell–Fokker–Planck equation, Liouville equation.
Keywords: steady state solution 
@article{IIGUM_2011_4_3_a11,
     author = {E. I. Semenov and A. V. Sinitsyn},
     title = {On a family of steady-state distributions of the {Vlasov{\textendash}Maxwell{\textendash}Fokker{\textendash}Planck} system},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {124--131},
     year = {2011},
     volume = {4},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIGUM_2011_4_3_a11/}
}
TY  - JOUR
AU  - E. I. Semenov
AU  - A. V. Sinitsyn
TI  - On a family of steady-state distributions of the Vlasov–Maxwell–Fokker–Planck system
JO  - The Bulletin of Irkutsk State University. Series Mathematics
PY  - 2011
SP  - 124
EP  - 131
VL  - 4
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/IIGUM_2011_4_3_a11/
LA  - ru
ID  - IIGUM_2011_4_3_a11
ER  - 
%0 Journal Article
%A E. I. Semenov
%A A. V. Sinitsyn
%T On a family of steady-state distributions of the Vlasov–Maxwell–Fokker–Planck system
%J The Bulletin of Irkutsk State University. Series Mathematics
%D 2011
%P 124-131
%V 4
%N 3
%U http://geodesic.mathdoc.fr/item/IIGUM_2011_4_3_a11/
%G ru
%F IIGUM_2011_4_3_a11
E. I. Semenov; A. V. Sinitsyn. On a family of steady-state distributions of the Vlasov–Maxwell–Fokker–Planck system. The Bulletin of Irkutsk State University. Series Mathematics, Tome 4 (2011) no. 3, pp. 124-131. http://geodesic.mathdoc.fr/item/IIGUM_2011_4_3_a11/

[1] E. I. Semenov, “O novykh tochnykh resheniyakh neavtonomnogo uravneniya Liuvillya”, Sib. mat. zhurn., 49:1 (2008), 207–217 | MR | Zbl

[2] K. Dressler, “Steady-states in plasma physics — the Vlasov–Poisson–Fokker–Planck equations”, Math. Methods in the Applied Sciences, 12 (1990), 471 | DOI | MR | Zbl

[3] R. Glassey, J. Schaeffer, Y. Zheng, “Steady-states of the Vlasov–Poisson–Fokker–Plank system”, J. of Math. Anal. and Applications, 202:3 (1996), 1058, 18 pp. | DOI | MR | Zbl

[4] N. Sidorov, B. Loginov, A. Sinithyn, M. Falaleev, Lyapunov–Schmidt Methods in Nonlinear Analysis and Applications, Kluwer Academic Publishers, 2002, 548 pp. | MR | Zbl

[5] E. I. Semenov, A. V. Sinitsyn, “New stationary distributions of the Vlasov–Maxwell–Fokker–Planck's system”, Physics Letters A, 374 (2010), 4222–4225 | DOI | MR | Zbl