Abstract
The stochastic linear Oskolkov model of oil transportation by the pipeline is represented by a set of linear one-dimensional Oskolkov equations, modeling the viscoelastic incompressible fluid flow. These equations are defined on the edges of a geometric graph with continuity and the flow balance conditions at its vertices. The deterministic model has been studied in various aspects by many mathematicians. The stochastic model is studied for the first time. The classical Ito–Stratonovich–Skorokhod approach, extended to the Hilbert spaces and the Sobolev type equations, is used as the method of the research. The main result is the theorem of unique solvability of the posed problem with additive white noise, which is understood as the generalized derivative of the \(K\)-Wiener process. The solution is represented in the form that allows to carry out the computational experiments.
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Notes
- 1.
A.A. Zamyshlyaeva, O.N. Tsyplenkova. Private communication.
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Zagrebina, S.A., Soldatova, E.A., Sviridyuk, G.A. (2015). The Stochastic Linear Oskolkov Model of the Oil Transportation by the Pipeline. In: Banasiak, J., Bobrowski, A., Lachowicz, M. (eds) Semigroups of Operators -Theory and Applications. Springer Proceedings in Mathematics & Statistics, vol 113. Springer, Cham. https://doi.org/10.1007/978-3-319-12145-1_20
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