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Information × Registration Number 0222U000107, 0121U110494 , R & D reports Title Nonlocal boundary value problems for degenerate partial differential equations and solutions with topological singularities of equations in Riemannian spaces popup.stage_title Head Kuz Anton M., Registration Date 03-01-2022 Organization Institute of Applied Problems of Mechanics and Mathematics named after Ya. S. Pidstryhach of the National Academy of Sciences of Ukraine popup.description2 Mathematical modeling of the interaction of fields of different physical nature, in particular gravitational and electromagnetic fields, is, today, an urgent task. Such modeling using analytical and computational methods is used in classical and quantum electrodynamics, quantum field theory, quantum chromodynamics and relativistic gravity theory. The aim of the project is to establish the conditions for the correct solvability of nonlocal boundary value problems for partial differential equations with power degeneracy of coefficients and to obtain new isotropic solutions of the system of vortex-type Maxwell equations in the Newman-Penrose formalism. Based on the results of the project, a scheme for splitting Maxwell's equations in Riemannian spaces in the case of an isotropic field is constructed. The split systems are considered in Kerr space-time, in planar space in the spherical coordinate systems. The conditions for the existence of a unique solution of problems with integral conditions on the selected variable for the equation with the Bessel operator in a bounded domain, for the Black-Scholes equation in the unbounded domain and for equations with partial derivatives of arbitrary order with power degeneracy of coefficients in the band. The solution of the problem in the form of a series is constructed for all problems; estimates of the lower denominators that arose during the construction of the solution are obtained. The results of research are theoretical and can be used in subsequent studies of nonlocal boundary value problems for equations and systems of partial differential equations with degeneracy. The results of the project research can be used to solve specific problems of practice, namely finding parameters and describing the propagation of isotropic electromagnetic fields near gravitational singularities. In particular, isotropic solutions can be used in powerless electrodynamics, in singular optics, in description of nodal fields, isotropic waves. Product Description popup.authors Taistra Yura V popup.nrat_date 2022-03-09 Close