|
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
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".
Received: 14.09.2017
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
Linking options:
https://www.mathnet.ru/eng/vyuru397 https://www.mathnet.ru/eng/vyuru/v10/i4/p5
|
Statistics & downloads: |
Abstract page: | 248 | Full-text PDF : | 94 | References: | 55 |
|