Search academic texts

Information × Registration Number 0214U006662, 0109U008762 , R & D reports Title Development of methods of solution and investigation of properties of nonlinear multidimensional integral and differential equations and their systems arising in problems with free phase and inverse scattering problems popup.stage_title Head Voytovych Mykola Mykolayovych, Savenko Petro Oleksandrovych, Registration Date 06-02-2014 Organization Pidstryhach Institute of Applied Problems of Mechanics and Mathematics NAS of Ukraine popup.description2 Main results: earlier approach to solving nonlinear integral equations of Hammerstein type associated with phase optimization problems, which is based on the representation of solutions by polynomials of finite powers, is extended to the case of the presence of zeros in the determining solutions region. The system of integral-transcendental equations for determination of parameters of these solutions and their branching points is obtained. The question of relationship between the sets of solutions of various types is investigated. The questions of the correctness of optimization problems performances with free phase are investigated and the conditions for their correct solvability are substantiated. The existence of solutions is proved and the numerical algorithms to find optimal solutions are proposed and justified for the variational problem of mean square approximation of real finite function by the modulus of double Fourier integral. To find the possible lines of solutions branching, the method based on the theory of implicit functions is proposed. The similar methods are developed for the problem of approximation of positive real finite function by the modulus of double discrete Fourier transform. For linear and nonlinear multi-parameter spectral problems, a variational approach is developed and iterative algorithms are constructed and justified. An algorithm that uses algebraic approach, which does not require calculating the coefficients of the characteristic equation, is also proposed. An asymptotic analytical-numerical method for solving the problem of scattering of electromagnetic waves on small bodies with the boundary conditions of the first (metal) and third (impedance) kind is developed in order to use it to build medium with desired properties. It is set the limits of using the asymptotic approach. For the problem of anti-planar deformation of solids with cracks system, the algorithm for determining the stress intensity factor in space with curvilinear cracks in the case of longitudinal shear in steady-state oscillation, which is based on the method of boundary integral equations, is proposed. The resonant frequencies for space weakened by system of cracks are investigated. Product Description popup.authors Андрійчук М.І. Булацик О.О. Войтович М.М. Заморська О.Ф. Кусий О.В. Подлевський Б.М. Савенко П.О. Соляр Т.Я. Ткач М.Д. Тополюк Ю.П. popup.nrat_date 2020-04-02 Close