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Registration Number

0220U103651, 0116U004084 , R & D reports

Title

The study of the asymptotic behavior of solutions of functional-differential equations and modeling of deterministic and stochastic applied processes

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Head

Cherevko Igor M., Доктор фізико-математичних наук

Registration Date

29-10-2020

Organization

Yuriy Fedkovych Chernivtsi National University

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For parabolic systems with singularity and increasing coefficients, as well as ultraparabolic equations of the Kolmogorov type, properties of fundamental solutions are investigated and classes of correctness of the Cauchy problem are described. The splitting of a linear two-tempo singularly perturbed system into independent subsystems is carried out, the principle of construction is established to study the stability of solutions of the initial system. Approximation schemes for systems of linear differential-difference equations of delay and neutral types are constructed and their application for approximation of nonsymptotic roots of quasipolynomials is considered. The conditions of the solution existence for boundary value problems with delay and neutral type are established, the approximation of their solutions using cubic splines of defect two is investigated and computer modeling is performed. The existence and stability of traveling waves in parabolic and differential-functional systems with low diffusion are studied. The conditions for the existence of a solution of the Cauchy problem for nonlinear stochastic differential-difference equations are established, and the stabilization of the strong solution of the autonomous stochastic Ito-Kolmogorov equation is investigated. All results presented in the report are new. They can be used both in theoretical research and in the substantiation of methods of solving and approximate solution construction for specific applied problems.

Product Description

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Ivasiuk Halyna P
Ilika Svitlana A
Haiuk Ivan M
Horbatenko Mykola Yu
Dorosh Andrii B
Doroshenko Iryna V
Klevchuk Ivan I
Lukashiv Taras O
Matvii Oleksandr V
Osypova Oleksandra V
Piddubna Larysa A
Pasichnyk Halyna S
Pertsov Andrii S
Tuzyk Iryna I
Fratavchan Tonia M
Cherevko Ihor M
Yurchenko Ihor V

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2020-10-29