| Autor: |
SUKACHEVA, T. G., ZAGREBINA, S. A. |
| Předmět: |
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| Zdroj: |
Global & Stochastic Analysis; Sep2024, Vol. 11 Issue 4, p166-177, 12p |
| Abstrakt: |
Recently, the theory of stochastic equations has been actively developing. Here it is worth noting the classical direction of research by Ito – Stratonovich – Skorokhod.Its main problem is to overcome the difficulties associated with the differentiation of a non-differentiable (in ”the usual sense”) Wiener process. It is also necessary to note the approach of I.V. Melnikova, within the framework of which stochastic equations are considered in Schwarz spaces using the generalized derivative. Our research will use methods and results of the theory, which is based on the concept of the Nelson – Glicklich derivative. Most studies consider the Cauchy problem for stochastic equations. In this article, instead of the Cauchy condition, it is proposed to consider a multipoint initial-final value condition. The obtained abstract results are used to analyze the solvability of the stochastic Oskolkov system, which models the dynamics of the velocity and pressure of a viscoelastic incompressible fluid. It is considered with a no-slip boundary condition and a multipoint initial-final value condition. The main result of the article is the proof of the solvability of the posed problem. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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