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Information × Registration Number 0216U005239, 0113U003030 , R & D reports Title Modelling and optimtzation of non-linear evolutionary system popup.stage_title Head Poliakov Nikolay Viktorovich, Registration Date 21-01-2016 Organization Dniepropetrovsk national university popup.description2 This project is focused on an optimal control problem for linear parabolic equations with unbounded coefficients in the principle part of elliptic operator, the model of quasi-static evolution of an internal damage in elastic bodies, and planetary systems.The project is aimed at the study of the solvability of optimal control problems in coefficients for degenerate parabolic systems, the development of asymptotic approach for the approximation of non-variational solutions for aforementioned optimal control problems, the study of optimal control problems for the mixed boundary value problem for an elastic body with quasi-static evolution of an internal damage, and the creation of general theory of formation and evolution of the planetary systems.The methods that were used in this project are advanced approaches of the theory of partial differential equations, functional analysis, and modern theory of optimal control problems. The main resulrs that were obtained in the framework of this project are the solvability conditions to optimal control problems for linear parabolic equations with unbounded coefficients, optimality conditions for such problems, and the existence of optimal and approximate solutions to the optimal control problem under rather general assumptions on the quasi-static evolution of internal damage. As for the novelty of the obtained results, this can be confirmed by their comparison with the results of other authors (Zhikov, Pastukhova, Robotnov, Kutler, Casado-Diaz, Buttazzo, Leugering, Horsin) where it has been emphasized the actuality and newness of these investigations. The main results of the project have been promoted into the educational process for students of Mechanics and Mathematics Faculty of Dnipropetrovsk National University. The main field of applications is the mathematical control theory and the qualitative analysis of dynamical systems. Product Description popup.authors Босенко Тимур Муртазович Горбонос Світлана Анатоліївна Клим Вікторія Юріївна Когут Петро Ілліч Меньшиков Юрій Леонідович Перехрест Володимир Іванович Сясєв Андрій Валерійович popup.nrat_date 2020-04-02 Close