Search academic texts

Information × Registration Number 0222U002585, 0119U101304 , R & D reports Title The initial-boundary value problems for partial differential equations: analysis, optimization, identification and their applications popup.stage_title Head Kogut Petrо I, Доктор фізико-математичних наук Registration Date 14-02-2022 Organization Oles Honchar Dnipro National University popup.description2   The objects of research are initial-boundary value problems for strongly degenerate hyperbolic equations, studt of its solvability, analysis of controllability problems when damage occurs at the boundary of the region, as well as developing a scheme for approximating the corresponding problems of optimal control of such systems.The aim of the work is to obtain new results in the field of qualitative analysis of initial-boundary value problems of mathematical physics and related optimization problems. Research methods - modern methods of the theory of differential equations in partial derivatives, methods of nonlinear functional analysis, the theory of optimization in normalized spaces, modern apparatus of nonparametric statistics, as well as the finite element method and variational methods.As a result of researches sufficient conditions of controllability of degenerate hyperbolic systems, conditions of their observation are received, the class of admissible distributions of destructions in one-dimensional area is described, the structure of approximation problems of management of such objects is received, new robust statistics - γ-weighted geometric mean are received.In addition, a mathematical model for calculating the thermal stress of spatial structures such as turbogenerator foundations in different operating conditions of power equipment was developed and an algorithm and method for solving the problem of determining the law of motion of the crystallization front and thermomechanical state of the body taking into account the interaction of temperature and mechanical fields. Scope: the results can be used in further research on the theory of optimal control and partial differential equations, which are conducted at the universities of Kiev, Lviv, Kharkiv, Naples, Salerno, Erlangen. Product Description popup.authors Borsch Volodymyr L. Horbonos Svitlana O Kogut Petrо I Siasiev Andrii V Turchyn Ievgen V Filipova Olga S popup.nrat_date 2022-03-09 Close