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Information × Registration Number 0211U009583, 0109U001456 , R & D reports Title Analytical methods in the qualitative theory of differential equations and in the control theory popup.stage_title Head Skljar G., Registration Date 30-12-2011 Organization Kharkov National University named after V.N. Karazin popup.description2 Object of the research - ordinary differential equations and partial differential equations, control 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. New bimodal approximate solution of the Boltzmann equation in the case when the discrepancy is chosen in a weighted space is obtained. For nonlinear kinetic Boltzmann equation in the case of the model of hard spheres the new approximate solution is found that ensures the infinitesimality of the uniform-integral weighted discrepancy between the sides of the equation and very fast tends to zero with increasing of the time.Solution of the exact controllability problem for a non-homogeneous Timoshenko beam model is obtained on the basis of the moment method by use of the spectrum asymptotics of the operator of the system. The complete description of sequences that are small growth vectors for nonlinear symmetric control systems is obtained and an algorithm for determining of the realizability of a sequence as a growth vector is given. The complete description of normal and simple growth vectors (in the sense of homogeneous approximation) for systems with two controls, normal forms of homogeneous approximations for such systems are found. A partial differential equation with discrete state-dependent delay is studied in the space of continuous functions; the new requirement for a delay is proposed that ensures the well-posedness of the initial value problem; for the case of initial functions from the Banach space, a small metric space is considered. Equations are studied in which two different types of delay (lumped and distributed) are present simultaneously; weak solutions of such equations are studied; the existence of a compact global attractor is proved. All results are new; they have theoretical and practical significance. They can be applied in the study of concrete mathematical problems as well as when solving of the problems arising in the mathematical modeling of real processes. The results and methods of research can be used in the work of the following scientific organizations: Institute of Mathematics of the National Academy of Sciences of Ukraine, Institute of Mathematics and Mechanics of the National Academy of Sciences of Ukraine, Kharkov, Kiev, Donetsk, Odessa Universities, Institute of Mathematics of the Russian Academy of Sciences, Institute of Applied Mathematics of the Russian Academy of Sciences, Friedrich-Alexander Universitat Erlangen-Nurnberg (Germany), University of Twente (The Netherlands), Szczecin University, Banach Center (Poland), International School for Advanced Studies (Italy), Universite Paris-7, Ecole Polytechnique, Ecole des Mines de Nantes (France), Autonomous University of the State Morelos (Mexico). NEUTRAL TYPE SYSTEMS, CONTROLLABILITY, MOMENT PROBLEM, BOLTZMANN EQUATION, BIMODAL SOLUTIONS, TIMOSHENKO BEAM MODEL, HOMOGENEOUS APPROXIMATION, NORMAL FORMS, EQUATION WITH DELAY, GLOBAL ATTRACTOR. Product Description popup.authors Ігнатович С. Гордевський В popup.nrat_date 2020-04-02 Close