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Izv. RAN. Ser. Mat., 2002, Volume 66, Issue 4, Pages 119–136 (Mi izv396)  

This article is cited in 4 scientific papers (total in 4 papers)

On finding moment functions for the solution of the Cauchy problem for the diffusion equation with random coefficients

V. G. Zadorozhniy

Voronezh State University

Abstract: 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.

DOI: https://doi.org/10.4213/im396

Full text: PDF file (270 kB)
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English version:
Izvestiya: Mathematics, 2002, 66:4, 771–788

Bibliographic databases:

UDC: 517.972
MSC: 35Q30, 46G10, 47A10, 58F30, 60H10
Received: 09.01.2001

Citation: V. G. Zadorozhniy, “On finding moment functions for the solution of the Cauchy problem for the diffusion equation with random coefficients”, Izv. RAN. Ser. Mat., 66:4 (2002), 119–136; Izv. Math., 66:4 (2002), 771–788

Citation in format AMSBIB
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\yr 2002
\vol 66
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\pages 119--136
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\jour Izv. Math.
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\pages 771--788
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. D. A. Grachev, “Tensor Approach to the Problem of Averaging Differential Equations with $\delta$-Correlated Random Coefficients”, Math. Notes, 87:3 (2010), 336–344  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. M. M. Borovikova, V. G. Zadorozhniy, “Finding the moment functions of a solution of the two-dimensional diffusion equation with random coefficients”, Izv. Math., 74:6 (2010), 1127–1154  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. T. V. Besedina, “Momentnaya funktsiya $n$-go poryadka resheniya zadachi Koshi dlya uravneniya diffuzii so sluchainymi koeffitsientami”, Vestn. SamGU. Estestvennonauchn. ser., 2011, no. 8(89), 5–20  mathnet
    4. D. A. Grachev, A. G. Zhdanov, “Modelirovanie nelineinogo rezhima dlya lagranzhevykh reshenii nekotorykh stokhasticheskikh evolyutsionnykh uravnenii”, Zh. vychisl. matem. i matem. fiz., 52:10 (2012), 1890–1903  mathnet
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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