Geodesic
On the connection between the solutions of the Boltzman and the Landau–Fokker–Planck equations
Sbornik. Mathematics, Tome 69 (1991) no. 2, pp. 465-478 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

It is proved that a solution of the Boltzmann equation in the limit case of scattering by small angles tends to a solution of the Landau–Fokker–Planck equation. 
@article{SM_1991_69_2_a9,
     author = {A. A. Arsen'ev and O. E. Buryak},
     title = {On the connection between the solutions of the {Boltzman} and the {Landau{\textendash}Fokker{\textendash}Planck} equations},
     journal = {Sbornik. Mathematics},
     pages = {465--478},
     year = {1991},
     volume = {69},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1991_69_2_a9/}
}
TY  - JOUR
AU  - A. A. Arsen'ev
AU  - O. E. Buryak
TI  - On the connection between the solutions of the Boltzman and the Landau–Fokker–Planck equations
JO  - Sbornik. Mathematics
PY  - 1991
SP  - 465
EP  - 478
VL  - 69
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1991_69_2_a9/
LA  - en
ID  - SM_1991_69_2_a9
ER  - 
%0 Journal Article
%A A. A. Arsen'ev
%A O. E. Buryak
%T On the connection between the solutions of the Boltzman and the Landau–Fokker–Planck equations
%J Sbornik. Mathematics
%D 1991
%P 465-478
%V 69
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1991_69_2_a9/
%G en
%F SM_1991_69_2_a9
A. A. Arsen'ev; O. E. Buryak. On the connection between the solutions of the Boltzman and the Landau–Fokker–Planck equations. Sbornik. Mathematics, Tome 69 (1991) no. 2, pp. 465-478. http://geodesic.mathdoc.fr/item/SM_1991_69_2_a9/

[1] Landau L. D., “Kineticheskoe uravnenie v sluchae kulonovskogo vzaimodeistviya”, Sobranie trudov, t. 1, Nauka, M., 1969, 199–207

[2] Lifshits E. M., Pitaevskii L. P., Fizicheskaya kinetika, Nauka, M., 1979 | MR | Zbl

[3] Rezibua P., De Lener M., Klassicheskaya kineticheskaya teoriya zhidkostei i gazov, Mir, M., 1980

[4] Bobylev A. V., “O razlozhenii integrala stolknovenii Boltsmana v ryad Landau”, DAN SSSR, 225:3 (1975), 535–538 | MR

[5] Skorokhod A. V., Stokhasticheskie uravneniya dlya slozhnykh sistem, Nauka, M., 1983 | MR

[6] Povzner A. Ya., “Ob uravnenii Boltsmana v kineticheskoi teorii gazov”, Matem. sb., 58(100) (1962), 62–86 | MR

[7] Arkeryd L., “On the Boltzman equation. P. I, II”, Arch. Rat. Mech. Anal., 45:1 (1972), 1–16 ; 17–34 | MR | Zbl | MR | Zbl

[8] Smirnova G. N., “Zadacha Koshi dlya parabolicheskikh uravnenii, vyrozhdayuschikhsya na beskonechnosti”, Matem. sb., 70(112) (1966), 591–604 | MR | Zbl

[9] Ladyzhenskaya O. A., Solonnikov V. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, Nauka, M., 1967

[10] Ilin A. M., Kalashnikov A. S., Oleinik O. A., “Lineinye uravneniya vtorogo poryadka parabolicheskogo tipa”, UMN, 17:3 (1962), 3–146 | MR