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Information × Registration Number 0223U001253, 0121U111949 , R & D reports Title Analysis of boundary-value problems in models of natural sciences popup.stage_title Head Pokutnyi Oleksandr O., Доктор фізико-математичних наук Registration Date 26-01-2023 Organization Institute of Mathematics of the National Academy of Sciences of Ukraine popup.description2 The aim of this work is to the study a wide class of boundary-value problems in various function spaces, in particular operator boundary-value problems for evolution systems of equations that arise in modeling of unstable irregular systems. We used methods of functional analysis, of the theory of linear operators and of the theory of semigroups of operators. For linear and nonlinear boundary-value problem in Hilbert and Banach spaces, we obtain a necessary and sufficient condition for solvability. Convergent iteration algorithms for construction of solutions to a nonlinear case are presented. We establish control conditions for not always solvable impulse systems of integro-differential equations. We find an expansion for the control and the solvability criterion for the system. We also consider a similar problem for a boundary-value problem for a system of integro-differential equations. We study systems of linear ordinary differential equations with the most general inhomogeneous boundary-conditions in arbitrary Sobolev spaces. We prove that these problems are Fredholm and found the indexes and dimensions of kernels and cokernels of the corresponding operators for these problems. We give several examples which show the constructive character of the obtained results. We also prove the possibility of approximation in Sobolev spaces of solutions to such problems by solutions to an explicitly constructed sequence of multipoint boundary-value problems with the same right-hand parts. For broad classes of general linear boundary-value problems for first order differential systems, in normalized Sobolev spaces and spaces of continuous functions, we obtain explicit estimates of the error of approximation of their solutions with solutions to sequences from broad classes of linear boundary-value problems. Product Description popup.authors Atlasiuk Olena Mykolaivna Bondar Ivanna Anatoliivna Soldatov Vitalii Oleksandrovych popup.nrat_date 2023-01-26 Close