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Information × Registration Number 0212U004187, 0107U000364 , R & D reports Title Investigation of the non-classical boundary-value problems for the partial differential equations and motion of charged particles in nonuniform media and fields. popup.stage_title Head Ptashnik Bogdan Yosypovych, Plyatsko Roman, Registration Date 31-01-2012 Organization Pidstryhach Institute for Applied Problems of Mechanics and Mathematics NASU popup.description2 The objects of the study of this report are boundary-value problems for partial differential equations, Dirichlet-periodic problem for linear hyperbolic one-dimensional hyperbolic systems of the first order with discontinuous coefficients and mixed problems for nonlinear ultraparabolic equations; coefficient inverse problems for one-dimensional parabolic equations in the domains with free boundaries, matrix polynomial equations over the number fields and combinatorial problems on graphs. The main results of the research: New approaches to the study of solvability and for building of the solutions to these problems, that are based on the methods of the theory of differential equations, the theory of analytic functions, functional analysis and metric number theory are proposed. The conditions of the existence and the uniqueness of solutions of the problem are proved. Equations of the Weyl and Dirac fields in the case of differential forms are generalized and the evolution of cosmological perturbations in models of the Universe with dark matter and reconstructed scalar field is studied. Solutions of the Mathisson-Papapetrou equations in the n Schwarzschild metric under the Matisona-Pirani and Tulczyjev-Dixon conditions are studied. The invariant inverse variational problem for ordinary differential equations of the third order are analysed. A method for modeling the evolution of the spectrum and radiation of relativistic particles on the fronts of the shock waves with an arbitrary angle between the normal and magnetic field is developed. The algebra of analytic block-symmetric functions on the Banach spaces with symmetric basis are investigated, a system of generators of algebra and algebraic dependence between these generators are descibed. The inverse problems of quantum scattering theory for one-dimensional Schr?dinger operators in the impedance form are investigated. The necessary and sufficient conditions for existence of solutions, such that their characteristic matrix have only two distinct invariant factors, for the matrix polynomial equations,over the field of the real numbers are shown, and the method of their creation is indicated. It is given the estimate of the number of solutions of matrix polynomial equations over the field of complex numbers, the characteristic roots of which have multiplicity two and it is established relationships between the number of solutions and the structure of the characteristic matrix of matrix equations. The new classes of solvable and insolvable matrix polynomial equations are found. We construct an algorithm for the complete sets of solutions of matrix polynomial equations with commuting coefficients. The descriptive complexity of graphs in special classes and computational complexity of combinatorial problems on graphs is investigated. Product Description popup.authors Білусяк Н.І. Вербіцький О.В. Власій О.Д. Гнатик Б.І. Гринів Р.О. Загороднюк А.В. Кміть І.Я. Мацюк Р.Я. Медвідь О.М. Пелих В.О. Петричкович В.М. Петрук О.Л. Пляцко Р.М. Процах Н.П. Пташник Б.Й. Симотюк М.М. Снітко Г.А. Шаваровський Б.З. Щедрик В.П. popup.nrat_date 2020-04-02 Close