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Vestnik Yuzhno-Ural'skogo Universiteta. Seriya Matematicheskoe Modelirovanie i Programmirovanie, 2017, Volume 10, Issue 4, Pages 5–14
DOI: https://doi.org/10.14529/mmp170401
(Mi vyuru397)
 

This article is cited in 7 scientific papers (total in 7 papers)

Mathematical Modelling

Some mathematical models with a relatively bounded operator and additive “white noise” in spaces of sequences

K. V. Vasyuchkova, N. A. Manakova, G. A. Sviridyuk

South Ural State University, Chelyabinsk, Russian Federation
Full-text PDF (553 kB) Citations (7)
References:
Abstract: The article is devoted to the research of the class of stochastic models in mathematical physics on the basis of an abstract Sobolev type equation in Banach spaces of sequences, which are the analogues of Sobolev spaces. As operators we take polynomials with real coefficients from the analogue of the Laplace operator, and carry over the theory of linear stochastic equations of Sobolev type on the Banach spaces of sequences. The spaces of sequences of differentiable "noises" are denoted, and the existence and the uniqueness of the classical solution of Showalter–Sidorov problem for the stochastic equation of Sobolev type with a relatively bounded operator are proved. The constructed abstract scheme can be applied to the study of a wide class of stochastic models in mathematical physics, such as, for example, the Barenblatt–Zheltov–Kochina model and the Hoff model.
Keywords: Sobolev type equations; Banach spaces of sequences; the Nelson–Gliklikh derivative; "white noise".
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 02.A03.21.0011
The work was supported by Act 211 Government of the Russian Federation, contract No. 02.A03.21.0011.
Received: 14.09.2017
Bibliographic databases:
Document Type: Article
UDC: 517.9
MSC: 60H30
Language: English
Citation: K. V. Vasyuchkova, N. A. Manakova, G. A. Sviridyuk, “Some mathematical models with a relatively bounded operator and additive “white noise” in spaces of sequences”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 10:4 (2017), 5–14
Citation in format AMSBIB
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\by K.~V.~Vasyuchkova, N.~A.~Manakova, G.~A.~Sviridyuk
\paper Some mathematical models with a relatively bounded operator and additive ``white noise'' in spaces of sequences
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2017
\vol 10
\issue 4
\pages 5--14
\mathnet{http://mi.mathnet.ru/vyuru397}
\crossref{https://doi.org/10.14529/mmp170401}
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\elib{https://elibrary.ru/item.asp?id=30752534}
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  • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Full-text PDF :94
    References:55
     
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