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Information × Registration Number 0307U001655, 0106U001561 , R & D reports Title Asymptotic and algebraic methods in the theory of differential equations and in the control theory popup.stage_title Дослідження асимптотичних та алгебраїчних властивостей різних класів динамічних систем Head Skljar G, Registration Date 18-04-2007 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 new analytic and algebraic methods in various fields of the quality theory of differential and functional-differential equations, optimal control theory for nonlinear and infinite-dimensional systems. Methods of the research - the general theory of differential equations, the control theory, functional analysis, algebra. Within the first part of the research: · For the case of the model of rigid spheres an approximate description of the interaction between two eddies (i.e. deformated non-stationary vortecies) is obtained. The integral remainder between the sides of the Boltzmann equation is used. Sufficient conditions of the infinitesimality of this remainder are found and their physical and geometrical sense is analysed; · The complete description of the privileged coordinates for the homogeneous approximation problem of affine control systems is given. The results are obtained byuse of the algebraic technique; · Null- and approximative controllability of the wave equation on the semi-axis with the control in the boundary condition is studied. Necessary conditions and sufficient conditions of null- and approximative controllability at the fixed time are obtained. A control which solves the null-controllability problem is found in the explicit form. The method of constructing of bang-bang controls is carried out; · The approach is suggested for study of PDE with state-dependent delay; the existence and uniqueness of weak solutions is proved, a dynamic system is constructed by these solutions, and the existence of the global attractor is proved. All results are new and have theoretical and practical value. They can be used for the investigation of concrete mathematical problems as well as for the solving of such problems that arise in the mathematical modelling of real processes. The results of the first part of the work are published in 5 works, 1 work is submitted to a mathematicaljournal. These results are presented in 3 reports at international scientific conferences. The results and the methods of the research can be used by the following scientific institutions: Institute of Mathematics (National Academy of Sciences of Ukraine), Institute of Mechanics and Applied Mathematics (National Academy of Sciences of Ukraine); Kharkov, Kiev, Donetsk, Odessa Universities; Institute of Mathematics (Russian Academy of Sciences), Institute of Applied Mathematics (Russian Academy of Sciences), Friedrich-Alexander Universitat Erlangen-Nurnberg (Germany), University of Twente (The Netherland), Szczecin University (Poland), Banach Center (Poland), Universite Paris-7 (France), International School for Advanced Studies (Italy), Ecole Polytechnique (France), Ecole des Mines de Nantes (France). MAXWELLIANS AND QUASIMAXWELLIANS, TORNADO FLOWS IN THE GAS OF RIGID BALLS, NONLINEAR CONTROL SYSTEMS, PRIVILEGED COORDINATES, WAVE EQUATION, EQUATION WITH STATE-DEPENDENT DELAY, GLOBAL ATTRACTOR. Product Description popup.authors popup.nrat_date 2020-04-02 Close