Geodesic
Mean field limit in a generalized Gibbs system and the equivalent nonequilibrium system of interacting Brownian particles
Teoretičeskaâ i matematičeskaâ fizika, Tome 76 (1988) no. 1, pp. 100-117 
V. I. Skripnik. Mean field limit in a generalized Gibbs system and the equivalent nonequilibrium system of interacting Brownian particles. Teoretičeskaâ i matematičeskaâ fizika, Tome 76 (1988) no. 1, pp. 100-117. http://geodesic.mathdoc.fr/item/TMF_1988_76_1_a8/
@article{TMF_1988_76_1_a8,
     author = {V. I. Skripnik},
     title = {Mean field limit in a~generalized {Gibbs} system and the equivalent nonequilibrium system of interacting {Brownian} particles},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {100--117},
     year = {1988},
     volume = {76},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1988_76_1_a8/}
}
TY  - JOUR
AU  - V. I. Skripnik
TI  - Mean field limit in a generalized Gibbs system and the equivalent nonequilibrium system of interacting Brownian particles
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1988
SP  - 100
EP  - 117
VL  - 76
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1988_76_1_a8/
LA  - ru
ID  - TMF_1988_76_1_a8
ER  - 
%0 Journal Article
%A V. I. Skripnik
%T Mean field limit in a generalized Gibbs system and the equivalent nonequilibrium system of interacting Brownian particles
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1988
%P 100-117
%V 76
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1988_76_1_a8/
%G ru
%F TMF_1988_76_1_a8

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

The mean field limit is found for weak solutions of the Bogolyubov–Strel'tsova diffusion hierarchy that at the initial time are identical to the Gibbs correlation functions. As a result, weak solutions of the nonlinear diffusion equation are found over a finite time interval.

[1] Chandrasekar S., Stokhasticheskie problemy v fizike i astronomii, IL, M., 1949

[2] Streltsova E. A., UMZh, 11:1 (1959), 83–92 | MR

[3] Bogolyubov N. N., Izbrannye trudy, T. 2, Naukova dumka, Kiev, 1970 | MR

[4] Maslov V. P., Kompleksnye markovskie tsepi i kontinualnyi integral Feinmana, Fizmatgiz, M., 1976 | Zbl

[5] Braun W., Hepp K., Commun. Math. Phys., 56:2 (1977), 101–113 | DOI | MR | Zbl

[6] Spohn H., Rev. Mod. Phys., 53:3 (1980), 569–615 | DOI | MR

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

[8] Kennedy T., Commun. Math. Phys., 92:2 (1983), 269–294 | DOI | MR | Zbl

[9] Fontaine J. R., Commun. Math. Phys., 103:2 (1986), 241–257 | DOI | MR | Zbl

[10] Skripnik V. I., TMF, 58:3 (1984), 398–420 | MR

[11] Skrypnik W. I., J. Stat. Phys., 38:5–6 (1984), 587–598 | DOI | MR

[12] Grewe N., Klein W., J. Math. Phys., 18:9 (1977), 1729–1734 | DOI

[13] Ginibre J., J. Math. Phys., 6:2 (1965), 238–262 | DOI | MR | Zbl

[14] Skripnik V. I., O skhodimosti ryadov teorii vozmuschenii dlya korrelyatsionnykh funktsii $S$-matritsy v nepolinomialnykh modelyakh pri beskonechnom evklidovom ob'eme, Preprint ITF-72-175E, ITF, Kiev, 1972

[15] Ryuel D., Statisticheskaya mekhanika. Strogie rezultaty, Mir, M., 1971

[16] Skripnik V. I., TMF, 69:1 (1986), 128–141 | MR

[17] Kac M., Uhlenbeck G., Hemmer P., J. Math. Phys., 4:2 (1963), 216–247 ; 5:1 (1964), 60–74 | DOI | MR | DOI | MR | Zbl

[18] Chueshov I. D., TMF, 67:2 (1986), 304–308 | MR