Search academic texts

Information × Registration Number 0219U000403, 0116U004691 , R & D reports Title Qualitative analysis of differential equations in abstract spaces using a simulation of physical processes popup.stage_title Head Zaporozhets Tetiana, Registration Date 29-01-2019 Organization B. Khmelnitsky state university in Cherkasy popup.description2 The object of research is the DE in abstract spaces, elliptic (right and wrongly elliptic) high-order distances, systems of two nonlinear degenerate parabolic equations of high order, diffusion processes. The research subject is the problems of stability, the existence and uniqueness of solutions of remote sensing in abstract spaces, initial problems with impulse influence, study of qualitative properties (existence, uniqueness, asymptotic behavior, investigation of regularity of solutions of limiting, non-classical problems for elliptic and parabolic DE). Main scientific results: New methods and approaches for constructing the Lyapunov auxiliary functionals for the study of the stability of the equilibrium of the SDE are developed. For a linear impulse system of a variable structure on the basis of the commutation calculus and the theory of the Lie algebra, we propose a method for constructing the Lyapunov function and obtain the conditions for the robustness of the switching law, which ensures the stability of the system. The necessary and sufficient conditions for asymptotic stability for linear periodic impulse systems with delay are established. The interval stability of a linear impulse system with delay under the very general assumptions about the dynamic properties of the continuous and discrete components has been studied. The stability of pseudo-linear impulse DE in a Banach space is studied and the obtained results are used to study the stability of a nonlinear system of ODE. A new method for investigating the stability of linear switched impulsive system in a Hilbert space based on the construction of an equivalent impulsive system without switching is proposed. The conditions of interval stability of a linear periodic switched impulsive system with a four-element structural set are established. New energy methods for studying singular solutions of general classes of quasilinear elliptic and parabolic equations that do not use any comparative technique are improved and developed. A new method for constructing the kernel of boundary problems has been developed and also were developed methods for determining the dimension of the kernel of boundary value problems for all classes of fourth-order incorrectly elliptic equations. Using the method of conformal mappings, we investigated the noetherianism of the Dirichlet and Neumann problems both for correctly elliptic equations and for all classes of incorrectly elliptic fourth-order equations. A stochastic medium-field method for modeling diffusion-controlled processes has also been developed. Product Description popup.authors Атамась Іван Володимирович Атамась Володимир Васильович Бівзюк Владислав Олегович Бойчук Олександр Андрійович Борисова Дарія Олександрівна Буряченко Катерина Олександрівна Гусак Андрій Михайлович Дем'яненко Ірина Олександрівна Денисенко Віктор Сергійович Денисенко Вікторія Олександрівна Кравчук Станіслав Вікторович Очеретнюк Євген Володимирович Ральченко Світлана Анатоліївна Слинько Віталій Іванович Тимошенко Богдан Віталійович Шишков Андрій Євгенович Яремченко Сергій Миколайович popup.nrat_date 2020-04-02 Close