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Information × Registration Number 0225U002725, (0124U001412) , R & D reports Title Asymptotic behavior, stability and controllability in infinite-dimensional evolutionary systems with deterministic and random perturbations popup.stage_title Асимптотична поведінка розв’зків еволюційних рівнянь параболічного типу та керованість. Head Stanzhytskyi Oleksandr M., Доктор фізико-математичних наук Registration Date 01-04-2025 Organization Taras Shevchenko National University of Kyiv popup.description1 The goal of the project is to study the global solvability, stability, and controllability of infinite-dimensional evolutionary problems with deterministic and random perturbations. The main attention will be paid to initial-boundary value problems for nonlinear equations in partial derivatives with non-autonomous, stochastic and impulse disturbances, establishment of conditions of global solvability and regularity, controllability, stability and robustness of attractors, functional stability of information systems. popup.description2 Theorems on the stability of attractors with respect to perturbations in sup-norms for nonlinear parabolic equations with external perturbations and perturbations on the boundary of the domain are proved. For systems of dynamic equations, theorems on the existence of periodic regimes and theorems on the relationship between periodic solutions of dynamic equations and systems of ordinary differential equations have been proved. Existence conditions were obtained and methods for approximate finding of optimal controls for infinite-dimensional systems with perturbations in coefficients based on the averaging method were developed. For stochastic functional-differential equations of neutral type, theorems on the existence of weak solutions are proved and their asymptotic behavior is studied. Theorems on the asymptotic equivalence of stochastic functional-differential equations to equations without delay are proved. For stochastic integro-differential equations of neutral type, theorems on the dependence of solutions on initial data in Sobolev norms have been obtained. The conditions for the functional stability of information networks used in the automation of production processes and information security systems described by discrete models with variable state vectors have been established. Product Description popup.authors Kapustian Oleksii V. Perestiuk Yurii M. Sobchuk Valentyn V. popup.nrat_date 2025-04-01 Close