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Information × Registration Number 0218U001528, 0116U000823 , R & D reports Title Studies in qualitative behavior of dynamical systems of various nature popup.stage_title Head Korobov Valeriy, Registration Date 12-03-2018 Organization Kharkov National University named after V.N. Karazin popup.description2 Report on the Scientific Research: 80 p., 2 tab., 16 fig., 85 ref. GLOBAL ATTRACTORS, FLUID-PLATE INTERACTION, UNIFORM STABILITY, INTEGRAL EQUATIONS, QUASI-OPTICAL SYSTEMS, DISCRETE VORTICES METHOD, FLOWS METHOD, ISOPERIMETRIC INEQUALITY, CONSTANT SLOPE CURVES Object of the research - dynamical systems arising in problems of the mathematical physics, the control theory, and the differential geometry. Aim of the research - creation of effective methods for the study of the qualitative behavior of solutions of interactive systems of evolution equations of the mathematical physics, study of three-dimensional diffraction boundary-value problems of electromagnetic waves, computing modeling of thermo-gas dynamics of cassettes in collectors of a nuclear reactor, study of connections of geometric and topologic properties of submanifolds. Methods of the research - methods of the general qualitative theory of differential equations, mathematical and functional analysis, mathematical physics, continuum mechanics. control theory, differential geometry and topology. Within the research: we prove the well-posedness in energy spaces (weak solutions) and more smooth spaces (strong solutions) for a number of problems of interaction of nonlinear elastic plates with different types of fluid; a mathematical model of quasi-optical splitter and combiner system is built on the base of singular and hypersingular integral equations, the discrete mathematical model is developed, a wide range of numerical experiments are calculated; a software is designed for computing modeling of thermo-gas dynamics of cassettes in collectors of a fast-neutron nuclear reactor and a wide range of numerical experiments are calculated; geometric invariants of curves in three-dimensional Lie groups are found which allow describing constant slope curves in such groups; the solution for the inverse isoperimetric inequality for convex surfaces of revolution by use of the control theory methods is obtained. 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 11 scientific papers, in 2 theses, in 31 contributions for international mathematical conferences, 13 papers are accepted and 4 papers are prepared for publication. Product Description popup.authors Є.Петров І.Рижкова-Герасимова В.Гордевський Г.Скляр К.Неесвіт М.Бебія М.Трощій Н.Кізілова О.Резуненко О.Соловйова О.Щербина С.Ігнатович С.Жученко С.Поцелуєв Т.Ревіна popup.nrat_date 2020-04-02 Close