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Information × Registration Number 0304U004083, 0103U004226 , R & D reports Title Analytical and algebraic methods in the theory of differential equations and control theory popup.stage_title Дослідження аналітичних та алгебраїчних структур, що виникають в теорії нелінійних керованих систем Head Skljar G., Registration Date 20-03-2004 Organization Kharkov National University named after V.N.Karazin popup.description2 Object of the research - ordinary differential equations and partial differential equations. Purposes - creating of 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 - moment problem, general theory of the differential equations, functional analysis, algebra. Within the first period: · The connection between the 0-controllability and e -controllability of the wave equation on a half-plane and infinite and finite Markov moment problem is given; · The conditions under which the solutions of two nonlinear time-optimal control problems are asymptotically equivalent in a neighborhood of the point of rest are obtained; · The model of the interconnection of two non-stationary (vortical) flows in a gas of rough spheres is constructed; · A class of approximate inertial manifolds which contain invariant sets of the dynamical system corresponding to the nonlinear partial differential equations is constructed. All results are new and have theoretical and practical value. They can be applied for the investigation of conctere mathematical problems as well as for solving the problems arising in mathematical modelling of real processes. The results of the first period of the research are published in 15 works, 3 papers are to appear. The results of the first period of the research are presented in 7 lectures on international science conferences.On the next period of the research the further sdudy of properties of solutions of differential equations by analytic and algebraic methods is supposed. Product Description popup.authors popup.nrat_date 2020-04-02 Close