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Information × Registration Number 0221U102425, 0116U000032 , R & D reports Title The development of operator approaches to solving evolutionary and spectral problems for differential equations popup.stage_title Head Kochubei Anatolii N., Доктор фізико-математичних наук Registration Date 02-02-2021 Organization Institute of Mathematics of the National Academy of Sciences of Ukraine popup.description2 Objects of research are linear and nonlinear differential and pseudodifferential equations that appear in models of mathematical physics. The purpose of the work is to study the problems of the theory of operators and related evolution equations, which are motivated by applications to the problems of mathematical physics. Methods are those of functional analysis, operator theories, fractional calculus, theories of kinematic variable sets. The results on the problems of functional analysis and operator theory, closely connected with the problems of mathematical physics, are presented. In particular, locally convex spaces are constructed in which an exponential representation of the analytical semigroup takes place; applications to a number of problems of analysis are given. The influence of the introduction of fractional derivatives in models of statistical mechanics on the properties of solutions of the corresponding evolution equations is investigated. The evolutionary equations of quantum theory and their applications, in particular, the hierarchies of evolution equations and nonlinear kinetic equations of complex systems, have been studied. The theory of kinematic variable sets and universal kinematics has been developed. Product Description popup.authors Artemichenko Zhanna Ya Herasymenko Viktor I Hrushka Yaroslav I Krechko Viktoria V Satur Oksana R popup.nrat_date 2021-02-02 Close