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Information × Registration Number 0219U102070, 0118U005389 , R & D reports Title Evolutionary boundary value problems and approximative properties of functional sets and their applications popup.stage_title Head Pokutnyi Oleksandr O., Registration Date 18-12-2019 Organization The Institute of Mathematics of NASU popup.description2  During the reporting period, the grant recipients worked in accordance with the research plans and obtained the following main results: The solution of the nonlinear boundary value problem with a small parameter, which turns into a solution of the generating linear boundary value problem, when the small parameter goes to zero, is found. Necessary and sufficient conditions for the solution of the corresponding boundary value problem are obtained in both linear and nonlinear cases. By means of a generalized Grin operator, solutions of the linear boundary value problem are constructed. For finding approximate solutions of the nonlinear equation, it is proposed to combine iterative algorithms of the Newton-Kantorovich type. The direct and inverse theorems for the approximation of functions of many Taylor-Abel-Poisson variables in integral metric are proved. Obtained by the order of estimation of the approximation of functions from the Nikol'skii-Bysov classes with dominant mixed derivative using entire functions of exponential type with carriers of their Fourier transform in the stepped hyperbolic cross. The necessary and sufficient conditions for the existence of solutions of a weakly nonlinear boundary value problem with impulse influence in the critical case of the second order are established, an iterative algorithm for construction of the solution is proposed. We find exact asymptotic equations for logarithmic energy and establish exact order estimates for the Riesz energies for sequences of well-distributed spherical t-designs on the d-dimensional sphere. Product Description popup.authors Bondar Ivanna A. Stepaniuk Tetiana A. Shidlich Andrii L. Yanchenko Sergiy Ya. popup.nrat_date 2020-04-02 Close