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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
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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/

[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