Some mathematical models with a relatively bounded operator and additive ``white noise'' in spaces of sequences
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 10 (2017) no. 4, pp. 5-14
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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".
@article{VYURU_2017_10_4_a0,
author = {K. V. Vasyuchkova and N. A. Manakova and G. A. Sviridyuk},
title = {Some mathematical models with a relatively bounded operator and additive ``white noise'' in spaces of sequences},
journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
pages = {5--14},
publisher = {mathdoc},
volume = {10},
number = {4},
year = {2017},
language = {en},
url = {http://geodesic.mathdoc.fr/item/VYURU_2017_10_4_a0/}
}
TY - JOUR AU - K. V. Vasyuchkova AU - N. A. Manakova AU - G. A. Sviridyuk TI - Some mathematical models with a relatively bounded operator and additive ``white noise'' in spaces of sequences JO - Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie PY - 2017 SP - 5 EP - 14 VL - 10 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/VYURU_2017_10_4_a0/ LA - en ID - VYURU_2017_10_4_a0 ER -
%0 Journal Article %A K. V. Vasyuchkova %A N. A. Manakova %A G. A. Sviridyuk %T Some mathematical models with a relatively bounded operator and additive ``white noise'' in spaces of sequences %J Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie %D 2017 %P 5-14 %V 10 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/VYURU_2017_10_4_a0/ %G en %F VYURU_2017_10_4_a0
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 Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 10 (2017) no. 4, pp. 5-14. http://geodesic.mathdoc.fr/item/VYURU_2017_10_4_a0/