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Information × Registration Number 0217U001263, 0116U000823 , R & D reports Title Studies in qualitative behavior of dynamical systems of various nature popup.stage_title Head Korobov Valeriy, Registration Date 02-02-2017 Organization Kharkov National University named after V.N. Karazin popup.description2 Object of the research - dynamical systems arising in problems of mathematical physics, fluid mechanics, control systems. Aim of the research - creation of effective methods for the study of the qualitative behavior of solutions of equations of the mathematical physics, creation of analytic methods for solving problems of stability, stabilizability, controllability, study of qualitative properties of solutions and construction of solutions for some classes of nonlinear and infinite-dimensional dynamical systems. Methods of the research - methods of the general and qualitative theory of differential equations, of the control theory, of the mathematical and functional analysis, of the mathematical physics, of the continuum mechanics. Within the research: the solutions of the problem of positional and robust synthesis of bounded controls, of the stabilizability and optimal control problems are obtained for some classes of nonlinear systems; the conditions for existence and the explicit form are obtained for some multi-modal and infinite-modal approximate solutions of nonlinear Boltzmann equation which ensure an arbitrary smallness of residual between sides of nonlinear Boltzmann equation, the method of construction of new classes of such solutions for the model of elastic spheres is proposed; the method of construction of a stability region in the physical parameter space is carried out for the system of two immiscible ferrofluids in the magnetic fields under the condition of boundedness of the free surface; the mathematical models of the pre-Cantor antennas based on boundary integral and pseudo-integral equations have been created and investigated; discrete models were developed using the quadrature formulas of interpolational type; comparative analysis have been carried out by the numerical experiments regarding to results what were obtained by other methods; the mathematical model described the fluid flow along a system of interconnected reservoirs accounting for the nonlinear properties of their walls is developed; the behavior of solutions of the corresponding systems of equations is studied; the ways and conditions for transition from regular to chaotic dynamics are described. All the results are new and have theoretical and practical significance. They can be applied in the study of concrete mathematical problems as well as in mathematical modeling of real processes. The results of the research are published in 27 scientific papers, 2 thesis, 1 preprint, in 22 contributions for international mathematical conferences, 7 papers are prepared for publication. Product Description popup.authors В. Гордевський К. Несвіт М. Бебія М. Пацегон О. Соловйова С. Ігнатович С. Поцелуєв popup.nrat_date 2020-04-02 Close