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Information × Registration Number 0305U003246, 0103U004226 , R & D reports Title Analytical and algebraic methods in the theory of differential equations and control theory popup.stage_title Дослідження певних задач теорії керування та стабілізації для нескінченновимірних систем Head Skljar G., Registration Date 03-03-2005 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 new analytical and algebraic methods in vartious areas of the quality theory of differential and functional-differential equations arising in the general theory of partial differential equations, optimal control theory for nonlinear and infinite-dimentional systems. Methods of the research - moment problem, general theory of differential equations, functional analysis, algebra. Within the second stage of the research: · Approximate null controllability of the wave equation on half plane with controlled by the bound conditions were investigated. Necessary and sufficient conditions at a given time of the control system considered were investigated; · The classification of nonlinear control systems in the neighborhood of the stationary point under general enough conditions on the control function were constructed; · Quasi-Maxwellians and local nonstationary Maxwellians which describe eddies in a gas of hard spheres are compared.; · The system of delay equations was investigated. The existence of inertial manifold with delay was proved. We showed that the system has the finite number of essential modes. All results are new and have theoretical and practical value. They can be used for the investigation of the concrete mathematical problems as well as for the solving of the problems arising in the mathematical modelling of real processes. The results of the work are published in 19, besides, 3 works are submitted to mathematical journals. These results are presented in 6 reports in international scientific conferences. On the next stage of the research it is supposed the following investigation of the properties of solutions of differential equations by use of analytical and algebraic methods. The results and the methods of the 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 University (Poland), Universite Paris-7 (France), Univ. di Roma ''La Sapienza'' (Italy). Product Description popup.authors popup.nrat_date 2020-04-02 Close