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Information × Registration Number 0203U008079, 0100U003350 , R & D reports Title Analytical methods in the theory of differential equations and control theory popup.stage_title Head Skljar G., Registration Date 22-04-2003 Organization Kharkov National University named after V.N.Karazin popup.description2 Object of the research - ordinary differential equations and partial differential equations. Aim of the work - to create and develop analytical methods for solving of the problems arising in the general theory of partial differential equations, optimal control theory, kinetic theory of multibody systems. Methods of the research - the general theory of partial differential equations, functional analysis, control theory, moment min-problem, theory of special functions, theory of symmetrization of analytic functions. Results obtained - within the research the new results are obtained in the following directions: - The representation of affine nonlinear control systems in the form of series of nonlinear power moments is analyzed; - The complete description of the solvability set for the trigonometric moment min-problem with gaps is given; - The control solving the problem of 0-controllability and approximate controllability for the wave equation on the semiaxis is found explicitly; - Positional controls stabilizing evolution equations and systems of partial differential equaitons on the whole space are found; - The problem of the strong stabilizability for the system with a skew-adjoint operator and one-dimensional control is considered; - Some classes of approximative explicit solutions of nonlinear kinetic Boltzmann and Bryan-Pidduck equations are constructed; - The exact estimate of the number of strong asymptotic places assotiated to a given point via the value of deviation is obtained; - The problem of construction of the inertial manifold with delay for the wide class of parabolic equations with the delay argument is considered. Novelty and recommendations for application - all results are new and have theoretical and practical value. They can be used for the further development of analytic methods for study of concrete mathematical problems as well as for solving of various problems arising in the mathematical modelling of real processes. The results of the work are published in 54 works (in particular in 1 monography), 10 works are submitted to mathematical journals. These results are presented in 14 reports at international scientific conferences. The results and the methods of the present research can be used by the following scientific institutions: Institute of Mathematics, Institute of Mechanics and Applied Mathematics (National Academy of Sciences of Ukraine); Kharkov, Kiev, Lvov, Donetsk Universities; Institute of Mathematics, Institute of Applied Mathematics (Russian Academy of Sciences), Technische Universitat Darmstadt (Germany), Beurauth Universitat (Germany), Szczecin Univ. (Poland), Universite Paris-7 (France), Univ. di Roma ''La Sapienza'' (Italy), Institut de Recherche en Communications et Cybernetique de Nantes (France). Product Description popup.authors popup.nrat_date 2020-04-02 Close