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Information × Registration Number 0221U105325, 0119U100334 , R & D reports Title Development of new analytic-geometric, asymptotic and qualitative methods for investigating invariant sets of divergent-objective equations. popup.stage_title Head Perestiuk Mykola O., Доктор фізико-математичних наук Registration Date 25-06-2021 Organization Taras Shevchenko National University of Kyiv popup.description2  Object of research: dynamic systems; parabolic systems; systems of nonlinear dynamics and polychaete oscillations; different classes of pulse systems, systems of differential equations; algebraic and topological systems. Purpose: to create new effective analytical and geometric algorithms for the study of current problems of modern theory of nonlinear evolutionary, stochastic, impulse systems, as well as algebraic systems, to obtain basic theoretical and practical statements. Research methods: analytical-geometric methods of analysis of nonlinear systems, method of normal forms, method of integral varieties, methods of global attractors, apparatus of nonlinear monotonic boundary value problems with boundary interaction, methods of differential geometry, categorical-algebraic and topological methods. The stability of uniform attracting sets for pulsed half-flows generated by pulsed-perturbed evolutionary systems with an unfixed set of images of pulsed reflection is investigated. The obtained results are applied to a weakly nonlinear parabolic system, the trajectories of which are subjected to impulse perturbation when the energy functional reaches the threshold definition. The conditions guaranteeing the hyperbolicity of systems of differential equations with impulse influence are established, the existence of bounded solutions of inhomogeneous multidimensional systems of differential equations with impulse perturbation is investigated. Nonlocal theorems of existence and uniqueness of weak solutions of infinite-dimensional stochastic systems with a nonlocal operator are established and their asymptotic behavior at infinity is studied. Qualitative behavior on infinite solutions of infinitely measurable stochastic evolution equations has been studied. Product Description popup.authors Asrorov Farkhod A. Vasylyk Olha I. Holovashchuk Nataliia S. Kapustyan Oleksiy Volodymyrovych Parasyuk Ihor O. Perestyuk Yuri М. Petravchuk Anatoliy P. Stanjuskyi Оleksandr M. popup.nrat_date 2021-06-25 Close