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Information × Registration Number 0219U004219, 0116U003590 , R & D reports Title Optimization of nonlinear systems with distributed parameters: qualitative analysis, approximation of solutions, optimality conditions popup.stage_title Head Kogut Petr Illich, Доктор фізико-математичних наук Registration Date 15-04-2019 Organization Oles Honchar Dnipro National University popup.description2 The object of the research is optimal control and optimization problems for elliptic boundary-value problems whose equations of state contain nonlinear operators of the type of generalized p (x) -lapsacian, in the presence of local and point phase constraints and control constraints. NDR aims to develop a general scheme for approximation of optimization and optimal control problems for quasilinear elliptic equations with generalized p (x) - Lapsacian in the main part of the operator and the relaxation scheme of phase constraints in the form of inclusions and inequalities that would solve the problem of reachability of optimal solutions and get a reasonable approach to the construction of necessary conditions for optimality of such problems. The task is to obtain new approximation results in Sobolev spaces with a variable exponent of optimal solutions of extremal problems for quasilinear elliptic equations with generalized p (x) - lapsacian. Substantiate the asymptotic scheme for constructing the necessary optimality conditions in the presented optimal control problems with phase constraints. Prove theorems on the solvability of such a class of problems and obtain a priori estimates for approximation sequences. The research method is modern methods of the theory of partial differential equations, variational methods of mathematical physics, functional analysis and mathematical control theory. Results of the work - a detailed qualitative analysis of optimal control problems for nonlinear elliptic systems containing the operator p (x) - lapsacian with a variable index p = p (x) was carried out, drawing on ideas from previous developments of P.I. Kogut, G. Leugering "a and E.Cassa'a.An important result of the work is the consideration of those problems where, if there are point-phase constraints, generalized solutions do not fit into the space of continuous functions in which the ordinal cone has a non-empty interior, which means attraction of the known rez According to this, an analogue of Tikhomirov's theorem is obtained concerning the necessary optimality conditions in such problems and their justifications are given. For the first time, the problem of optimal control of a thermistor in its general formulation has been solved. Novelty of the development - the obtained results are new, which is confirmed by their comparison with the works of well-known experts (Zhikov, Shepherds, Robotnov, Kutler, Casado-Diaz, Buttazzo, Horsin, Leugering), which emphasize that the chosen direction of research is relevant and new. The results of research have been introduced into the educational process for students of the Faculty of Mechanics and Mathematics of the DNU The main field of application is mathematical control theory and qualitative analysis of dynamic systems. Product Description popup.authors Mеньшиков Юрій Леонідович Баланенко Iрина Григорівна Бира Тетяна Станіславівна Борщ Володимир Леонідович Горбонос Світлана Олексіївна Д'яченко Михайло Павлович Макаренков Євген Анатолійович Матяш Марина Вікторівна Поляков Микола Вікторович Совіт Юрій Петрович Сясєв Андрій Валерійович Турчин Євген Валерійович Філіпова Ольга Сергіївна popup.nrat_date 2020-04-02 Close