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Information × Registration Number 0214U007988, 0111U010369 , R & D reports Title Analysis of evolution problems with Sobolev equations popup.stage_title Head Rutkas Anatoly, Registration Date 19-01-2015 Organization Kharkov National University named after V.N. Karazin popup.description2 Investigation object - evolution problems for different classes of Sobolev operator differential equations in Banach and Hilbert spaces with unbounded operator coefficients, in particular, impulsive equations, functional differential equations, stochastic equations. Work purpose - to investigate spectral properties of characteristic operator sheaves, resolvents and pseudoresolvents, which correspond to Sobolev equations; to investigate spectral Riesz projectors and projectors as weak limits of pseudoresolvents; to show the connection between spectral properties of corresponding operators and operator functions and the solvability of evolution problems; to realize applications to partial differential equations and applied problems. Investigation methods - the spectral analysis of operators and operator sheaves, the analytic properties of resolvent operator functions, the theory of analytical and meromorphic operator functions, the optimization methods in Hilbert spaces, the stochastic analysis, the convex analysis, the theory of multivalued manifolds, the theory of partial differential equations. Main results: - new theorems for Sobolev operator differential equations with impulses, with delay, for stochastic operator differential equations, for functional differential equations; - new statements for different classes of partial differential equations not of Kovalevskaya type and differential algebraic equations. Product Description popup.authors Власенко Л. Забара О. Півень О. Руткас А. Філіпковська М. popup.nrat_date 2020-04-02 Close