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Information × Registration Number 0222U005384, 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 29-12-2022 Organization Institute of Applied Problems of Mechanics and Mathematics named after Ya. S. Pidstryhach of the National Academy of Sciences of Ukraine popup.description2  During the research, a scheme for splitting Maxwell equations in Riemannian spaces in the case of an isotropic field was constructed. Split systems are written in Kerr space-time, where the isotropic tetrad is the Kinnersley tetrad, in Schwarzschild space-time in Schwarzschild coordinates, and in flat space in spherical, Cartesian, cylindrical coordinate systems. In the spinor approach, a subclass of isotropic fields is considered, which is built on the basis of some background isotropic field. Unlike the general case of an isotropic field, in this subclass of fields the electromagnetic background field satisfies Maxwell equations, which is an additional condition on the field function. This additional condition allows us to obtain a splitting scheme with simpler equations than in the general case of an isotropic field. The correctness of problems with integral conditions in the form of moments of arbitrary order in chosen variable for an equation with a Bessel operator in a bounded domain, for a Trichomy-type equation in a semi-bounded domain, and for PDE and systems of PDE with power-law degeneracy of coefficients in the strip is investigated. The correctness conditions of the problem with an integral condition for the Black-Scholes equation in an unbounded domain have been established. For all problems, the solution of the problem is built in the form of a series; estimates from below of the small denominators that arose during the construction of the solution were obtained, and the problem cases in which there is no problem of small denominators were selected. The research results are theoretical in nature and can be used in further studies of nonlocal boundary value problems for PDE and systems of PDEs with degeneracies. The results of the project can be used to solve specific practical problems, namely, finding the parameters and describing the distribution of isotropic electromagnetic fields near gravitational singularities. Product Description popup.authors Taistra Yurii V. popup.nrat_date 2022-12-29 Close