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Information × Registration Number 0211U002374, 0109U006435 , R & D reports Title Constructive investigation methods and stabilization for evolution equations popup.stage_title Head Perestyuk Mykola Oleksiyovych, Доктор фізико-математичних наук Registration Date 04-02-2011 Organization Taras Shevchenko Kiev university popup.description2 In work the method of averaging for optimum control problems by nonlinear finite-dimensional process on a semi-axis and a segment is proved. For a class of problems, linear on control, results of existence of the solution of exact system are received; conditions at which optimum control of average system provides near optimal behavior of an exact problem are found. For a problem of the optimum bounded control for weakly nonlinear boundary-value problem of parabolic type, in case of a control reach the restrictions, existence of optimum synthesis which implement control of system in a mode, near optimal is established. On the basis of exact synthesis of unperturbed problem of optimum control for evolutionary inclusion of subdifferential type the approached synthesis of an initial problem which is perturbed with the multiple-valued summand is proved. For the stochastic differential equation, unsolvable with respect to stochastic differential from a phase variable, solution definition is offered, the existence and uniqueness theorem is established, is proved that the solution is Markovian process, conditions diffused this process and it diffused coefficients are found. For systems of difference equations with a constant deviation of argument conditions of existence and uniqueness of the continuous periodic solutions, and also, existence of the continuous bounded solutions are received; under condition of existence of periodic solutions the behavior on infinity of solutions of considered systems is studied. For a wide class of systems the difference equations it is offered procedure of construction of set of continuous solutions. For systems the linear functionally- difference equations existence conditions of continuous periodical solutions are received and the structure of set of solutions is investigated. For system the nonlinear functionally- difference equations existence conditions continuous and bounded on all axis and on positive and negative semi-axes of solutions are found and the structure of set of all such solutions is studied. The functional-topological properties of the solving operator of differential-operational inclusion of the second order are studied with weakened coercitive, pseudo-monotonous mapping is studied. The behavior of solutions of the autonomous equation of reaction-diffusion with multiple-valued nonlinearity is investigated, aprioristic estimations are received and existence global attractor for a multiple-valued half-flow is proved. Product Description popup.authors Капустян Олексій Володимирович Касьянов Павло Олегович Парасюк Ігор Остапович Пелюх Григорій Петрович Перестюк Микола Олексійович Самойленко Анатолій Михайлович Станжицький Олександр Миколайович Сукретна Анна Василівна popup.nrat_date 2020-04-02 Close