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Information × Registration Number 0222U001131, 0117U002119 , R & D reports Title Analytical and group methods for investigation of mathematical models of modern science popup.stage_title Head Boichuk Oleksandr A, Доктор фізико-математичних наук Registration Date 24-01-2022 Organization Institute of Mathematics of the National Academy of Sciences of Ukraine popup.description2 The report on research on "Analytical and group methods for investigation of mathematical models of modern science" contains 346 pages, 19 sections. The results of research on the topic have been published in 94 papers. Object of research: nonlinear systems of ordinary differential equations, difference equations and equations with impulse action, integrable dynamical systems, boundary-value problems for functional-differential equations, systems of coupled oscillators, linear and nonlinear differential and pseudo-differential equations that appear in models of mathematical physics. Purpose: study of equilibrium, oscillatory and transient processes in mathematical models of science by analytical and group methods, development of spectral and evolutionary methods of research of models of modern mathematical physics, study of inverse spectral problems for metric and quantum graphs, development of effective methods and algorithms for solving inverse scattering for wave equations, development of non-Archimedean and operator methods for studying some evolution processes in physics, mechanics and biology. Research methods: qualitative, numerical-analytical, spectral, variational, group and other methods of analysis of solutions of differential and functional-differential equations, methods of bifurcation theory and their application to the theory of coupled oscillators, inverse operators, methods of potential theory, etc. The research conducted on the reporting topic is fundamental. The obtained results meet high international standards and make a significant contribution to the development of the theory of differential equations, mathematical physics and functional analysis. Product Description popup.authors popup.nrat_date 2022-03-09 Close