Zhumabayeva A.2026-10-292026-10-292026Zhumabayeva A / Applications of Otelbaev's Abstract Theorem to singular ODES / SDU University / Department of Mathematics and Natural Scienceshttps://repository.sdu.edu.kz/handle/123456789/2700This research focuses on analyzing well-posedness of a singular hyperbolic equation with time-varying coefficients, defined on a multidimensional cylindrical domain. Using the spectral decomposition method, the original problem was reduced to a family of one-dimensional singular differential equations. Furthermore, a comprehensive matrix representation of all regular regular boundary conditions is derived through the M. Otelbaev’s abstract theorem and the Riesz theorem. Finally, the existence and uniqueness of the solution for the original two-dimensional equation is established in the within weighted Sobolev space.enSingular equationSobolev Regularity for the Singular ODEDegenerate Hyperbolic EquationThesis