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Information × Registration Number 0214U007983, 0111U010364 , R & D reports Title Analytic methods for solving qualitative problems of the control theory and of the theory of functional-differential equations popup.stage_title Head Sklyar Grigory, Registration Date 19-01-2015 Organization Kharkov National University named after V.N. Karazin popup.description2 Object of the research - dynamical and control nonlinear and infinite-dimensional systems. Aim of the research - creation of new analytic methods in various fields of the quality theory of differential and functional-differential equations, the optimal control theory for nonlinear and infinite-dimensional systems. Methods of the research - the methods of the general and qualitative theory of differential equations, the control theory, the mathematical and functional analysis, algebra. Within the research: On the way of developing the approach based on "the ignoring condition" for a delay for PDE with discrete state-dependent delay, the questions of the well-posedness are studied; a wide class of state-dependent delays is investigated; asymptotic properties of solutions and conditions for existence of a global attractor are studied. On the way of developing the methods of generalized trigonometric moment problem the optimal control problem for non-homogeneous vibrating systems is solved. Continual analogues for bimodal distributions for a model of hard spheres are constructed; the interaction of eddy flows is studies with the help of the Bryan-Pidduck equation. The time-optimal problem for nonlinear affine symmetric control systems and properties of optimal controls are studied; the connection between approximations in the sense of time optimality and in the sense of sub-Riemannian metrics is described. A description of regular symmetric systems is given in terms of the corresponding series of iterated integrals. The asymptotic behavior of solutions and the controllability are studied for delay systems of neutral type. All results are new and have theoretical and practical significance. They can be applied in the study of concrete mathematical problems as well as when solving problems arising in the mathematical modeling of real processes. The results of the research are published in 22 scientific papers, 22 contributions for international mathematical conferences are prepared. Product Description popup.authors Ігнатович С. Гордевський В. Марченко В. Ніколенко І. Резуненко О. Скляр Г. popup.nrat_date 2020-04-02 Close