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Information × Registration Number 0121U109525, ( 0221U107201  0223U001288  0223U005637  ) R & D request Title Spectral problems and regularity properties of differential and integral operators, boundary value problems for planar structures Head Derkach Volodymyr O., Доктор фізико-математичних наук Registration Date 11-03-2021 Organization Vasyl' Stus Donetsk National University popup.description1 The aim of the project is to develop functional methods for the theory of extensions of symmetric operators, to develop a method for solving the Korteweg-de Vries equation using inverse scattering problems for Schrödinger operators, to develop new methods for studying qualitative properties of elliptic and parabolic equations with nonstandard growth conditions. theories and principles of operation of active and passive devices of the microwave frequency range based on multilayer planar structures; development and improvement of samples of high-efficiency transmitters (oscillators) for communication systems. Main tasks: development of new methods and obtaining new fundamental results in the field of spectral problems of operators, elliptic and parabolic equations with nonstandard conditions: construction of new functional models of integer symmetric operators, research of regularity of critical points for indefinite integrated systems, research of Schrödinger operators integrable on the half-axis, and the corresponding generalized soliton solutions of the Korteweg – de Vries equation, modification of the methods of Moser, De Giorgi, Kilpelainen-Maly, introduction of new B_1-classes, new method of energy estimates, generalized Zhikov condition, regularity analysis, exact analysis, exact qualitative behavior of solutions such as potential. Development of mathematical methods in applied problems for individual oscillating processes: description of processes in broadband amplifiers and high-efficiency autogenerators with complex spectrum and mode change. popup.nrat_date 2024-12-09 Close