Search academic texts

Information × Registration Number 0226U002273, (0124U001412) , R & D reports Title Asymptotic behavior, stability and controllability in infinite-dimensional evolutionary systems with deterministic and random perturbations popup.stage_title Імпульсні еволюційні системи, керованість та стохастичні рівняння дифузійного типу. Head Stanzhytskyi Oleksandr M., Доктор фізико-математичних наук Registration Date 12-02-2026 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 Within this project, we study the global solvability, asymptotic behavior, stability, and controllability of infinite-dimensional evolution problems under deterministic and stochastic perturbations. The central objects of the study were initial–boundary value problems for nonlinear partial differential equations with nonautonomous, stochastic, and impulsive perturbations, as well as systems of integro-differential equations and systems of functional differential equations. The following tasks were carried out: 1) For nonlinear parabolic equations with external and impulsive perturbations, using the general theory of attractors, sufficient conditions for the existence of attracting sets of a coefficient-type nature were obtained; moreover, by means of the input-to-state stability theory, the continuous dependence of attractors on external perturbations in the sup norm was established. 2) Minimax estimation of the parameters describing external disturbing factors was carried out based on fixed-point methods; 3) Asymptotic expansions were constructed and asymptotic estimates were obtained for singularly perturbed equations with degeneration in the highest derivative, using the ideas of the Bazov method and employing the technique of decomposing the solution into regular and singular parts of a boundary-layer type. 4) The averaging method was applied to optimal control problems for infinite-dimensional evolution systems and inclusions, as well as for systems of integro-differential equations with rapidly oscillating coefficients, which allowed reducing the study of optimal control problems to the analysis of simpler structures: autonomous evolution systems and systems of ordinary differential equations. The results concerning the asymptotic closeness of the solutions of the original problems and the corresponding solutions of the averaged systems were established. Product Description popup.authors Oleksiy V. Kapustyan Yurii M. Perestiuk Valentyn V. Sobchuk Nina V. Kasimova popup.nrat_date 2026-02-12 Close