Geodesic
On finding moment functions for the solution of the Cauchy problem for the diffusion equation with random coefficients
Izvestiya. Mathematics, Tome 66 (2002) no. 4, pp. 771-788 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the Cauchy problem for the diffusion equation with one spatial variable. The coefficients and the initial data are random processes. Formulae for the first and second moment functions are derived for the solution of the problem. 
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V. G. Zadorozhniy. On finding moment functions for the solution of the Cauchy problem for the diffusion equation with random coefficients. Izvestiya. Mathematics, Tome 66 (2002) no. 4, pp. 771-788. http://geodesic.mathdoc.fr/item/IM2_2002_66_4_a3/

[1] Danford N., Shvarts D., Lineinye operatory, I, IL, M., 1962

[2] Vladimirov V. S., Obobschennye funktsii v matematicheskoi fizike, Nauka, M., 1976 | MR | Zbl

[3] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1976 | MR

[4] Zadorozhnii V. G., Differentsialnye uravneniya s variatsionnymi proizvodnymi, VorGU, Voronezh, 2000 | MR | Zbl

[5] Klyatskin V. I., Stokhasticheskie uravneniya i volny v sluchaino-neodnorodnykh sredakh, Nauka, M., 1980 | MR | Zbl

[6] Fursikov A. V., “Problema zamykaniya tsepochek momentnykh uravnenii, sootvetstvuyuschikh trekhmernoi sisteme uravnenii Nave–Stoksa v sluchae bolshikh chisel Reinoldsa”, DAN SSSR, 319:1 (1991), 83–87 | MR | Zbl

[7] Fursikov A. V., “Momentnaya teoriya dlya uravnenii Nave–Stoksa so sluchainoi pravoi chastyu”, Izv. RAN. Ser. matem., 56:6 (1992), 1273–1315 | MR | Zbl

[8] Shapiro V. E., Loginov V. M., Dinamicheskie sistemy pri sluchainykh vozdeistviyakh, Nauka, Novosibirsk, 1983

[9] Tikhonov V. I., “Vozdeistvie fluktuatsii na prosteishie parametricheskie sistemy”, Avtomatika i telemekhanika, 19:8 (1958), 717–723

[10] Adomian Dzh., Stokhasticheskie sistemy, Mir, M., 1987 | MR

[11] Venttsel A. D., Freidlin M. I., Fluktuatsii v dinamicheskikh sistemakh pod deistviem malykh sluchainykh vozmuschenii, Nauka, M., 1979 | MR | Zbl

[12] Monin A. S., Yaglom A. M., Statisticheskaya gidromekhanika, Ch. 2, Nauka, M., 1967

[13] Zadorozhnii V. G., Stroeva L. N., “O momentnykh funktsiyakh resheniya nachalnoi zadachi lineinogo differentsialnogo uravneniya pervogo poryadka so sluchainymi koeffitsientami”, Differents. uravn., 36:3 (2000), 377–385 | MR | Zbl

[14] Zadorozhnii V. G., “Differentsialnoe uravnenie v banakhovom prostranstve, soderzhaschee variatsionnuyu proizvodnuyu”, SMZh, 33:2 (1992), 80–93 | MR | Zbl

[15] Zadorozhnii V. G., “Momentnye funktsii resheniya zadachi Koshi stokhasticheskogo uravneniya teploprovodnosti”, Dokl. RAN, 364:6 (1999), 735–737 | MR | Zbl

[16] Shilov G. E., Matematicheskii analiz. Vtoroi spetsialnyi kurs, Nauka, M., 1965 | MR