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Information × Registration Number 0219U001420, 0116U001525 , R & D reports Title Optimization of non-linear systems with distributed parameters: qualitative analysis, solutions aproximation, optimality conditions popup.stage_title Head Kogut Petro Illitch, Доктор фізико-математичних наук Registration Date 29-01-2019 Organization Oles Honchar Dnipro National University popup.description2 The object of investigation is optimization problems and optimal control problems with control and pointwise state constraints for quasi-linear elliptic equations containing in their principle part the p-Laplacian with variable exponent p=p(x).The main aim is to develop a general approximation scheme of optimal control problems for quasi-linear elliptic equations with generalized p(x)-Laplacian in their principle part and propose a relaxation approach to the approximation of the inequality state constraints in order to study the attainability of optimal pairs to the original problems and derive the optimality conditions passing to the limit in optimality conditions for regularized problems.The investigation methods include different approaches of the modern theory of partial differential equations, variational methods, methods of the functional analysis and mathematical control theory.The main issues that have been studied in the framework of this project: it was provided a substantial analysis of a wide class of optimal control problems for quasi-linear elliptic equations with generalized p(x)-Laplacian in their principle part; it was considered a class of optimal control problems with the pointwise state constraints for which the ordering cone is non-solid for which the standard multiplier rule, which gives a necessary optimality condition, cannot be applied; using the so-called Henig approximation of ordering cones, it was proven a generalization of the well-known Tikhonov theorem; it was studied and solved, for the first time, the optimal control in coefficients for the system of two coupled non-linear elliptic equations also known as thermistor problem.The main realm for application is the mathematical control theory and qualitative analysis of dynamical systems. Product Description popup.authors Баланенко Ірина Григорівна Горбонос Світлана Анатоліївна Дзюба Олександр Анатолійович Клим Вікторія Юріївна Коновал Тетяна Сергіївна Купенко Ольга Петрівна Меньшиков Юрій Леонідович Путченко Анна Олександрівна Сясєв Андрій Валерійович Ткаченко Павло Ігорович Шевельова Алла Євгенівна popup.nrat_date 2020-04-02 Close