Geodesic
The Initial-Final Value Problem for the Linear Stochastic Hoff Model
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 7 (2014) no. 2, pp. 124-128

Voir la notice de l'article provenant de la source Math-Net.Ru

The stochastic linear Hoff model of buckling of I-beam constructions amounts to a set of linear one-dimensional Hoff equations defined on the edges of a geometric graph with continuity and balance-of-flows conditions at its vertices. The deterministic model has been studied in various aspects by many mathematicians. We study the stochastic model for the first time. Our tool is the classical Ito–Stratonovich–Skorokhod approach extended to Hilbert spaces and Sobolev-type equations. The main result is an existence and uniqueness theorem for solutions to the initial-final value problem with additive white noise, understood as the generalized derivative of the $K$-Wiener process. The formulas expressing the solution are suitable for computer simulations.
Keywords: initial-final value problem; linear Hoff equations; stochastic Sobolev-type equations; geometric graph; Wiener process; additive white noise. 
@article{VYURU_2014_7_2_a11,
     author = {E. A. Soldatova},
     title = {The {Initial-Final} {Value} {Problem} for the {Linear} {Stochastic} {Hoff} {Model}},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {124--128},
     publisher = {mathdoc},
     volume = {7},
     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2014_7_2_a11/}
}
TY  - JOUR
AU  - E. A. Soldatova
TI  - The Initial-Final Value Problem for the Linear Stochastic Hoff Model
JO  - Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie
PY  - 2014
SP  - 124
EP  - 128
VL  - 7
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VYURU_2014_7_2_a11/
LA  - ru
ID  - VYURU_2014_7_2_a11
ER  - 
%0 Journal Article
%A E. A. Soldatova
%T The Initial-Final Value Problem for the Linear Stochastic Hoff Model
%J Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie
%D 2014
%P 124-128
%V 7
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VYURU_2014_7_2_a11/
%G ru
%F VYURU_2014_7_2_a11
E. A. Soldatova. The Initial-Final Value Problem for the Linear Stochastic Hoff Model. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 7 (2014) no. 2, pp. 124-128. http://geodesic.mathdoc.fr/item/VYURU_2014_7_2_a11/